Question Class XCBSE physics

Class – X Sub: - Physics F.M -100 

Section – A 

Choose the correct alternative ( MCQ) 1 x 25 = 25 

Q 1. What is the SI unit of power of a lens ? a) Watt b) Diopter c) Lumen d) Meter 

Q2 ,Which material is non- magnetic ? a) Iron b) Nickel c) Copper d) Cobalt 

Q3. The resistance of a wire of length L and cross-sectional area is R . What is the new resistance if length is doubled and area is halved ? a) R/2 b) 2R c) 4R d) R/4 

Q4 . The change in the direction of a wave passing from one medium to another is termed as ---------- a) Interference b) Mirage c) Diffraction d) Refraction 

Q5 what would be the angle of incidence for a light ray having zero reflection angle ? A) 180 degree b) 90 degree c) 0 degree d) 45 degree 

Q6. A full length of the image of a distant tall building can be seen using ----------- a) a convex mirror b) a plane mirror c) a concave mirror d) none of the options 

Q7 . The ratio of the sine of the angle of incidence to the the sine of the angle of refraction is constant . It is given by --------- a) Faraday’s law b) Snell’s law c) Newton’s law d) Murphy’s law 

Q8 . Electrical resistivity of a metallic wire depends upon its -------a) Length b) Material c) Thickness d) Shape 

Q9 . Electrical current is measured using ----------- a) Galvanometer b) Ammeter c) Voltmeter d) Potentiometer 

Q10 . Materials which do not allow electricity to pass through are known as ---------- a) Semiconductor b) Conductor c) Insulator d) Semi-insulator 

Q11. Copper is used in electric transmission lines because it has ----------- a) High resistivity b) Low resistivity c) No resistivity d) None of the option 

Q12 . Magnetic field lines emerge from a) South pole b) North pole c) Centre of magnet d) None of the option 

Q13 . Magnetic field is a a) Scalar quantity b) Vector quantity c) Dimensionless quantity d) None of the option 

Q14. Which of the following is used to detect the presence of current in a circuit ? a) Meter bridge b) Sonometer c) Galvanometer d) Electric motor 

Q15. The force exerted on a current carrying wire placed in a magnetic field is zero when the angle between the wire and the direction of the magnetic field is -------- a) 180 m degree b) 45 degree c) 90 degree d) 60 degree 

Q16. Unit of electric power may also be expressed as a) Watt second b) Ampere hour c) Volt ampere d) Kilowatt hour 

Q17 . How does the eye change in order to focus on near or far objects ? a) The lens moves in or out b) The pupil gets smaller c) The retina moves in or out d) The lens becomes thicker or thinner 

Q18. The crystalline lens of people at bold age becomes milky and cloudy , this condition is known as -------- a) Hypermetropia b) Myopia c) Cataract d) Presbyopia 

Q19 . In the rearview mirror of the vehicle what will be the magnification ? a) 1 b) greater than 1 c) less than 1 d) No magnification seen 

Q20 . In which of the following does light travel fastest ? a) Oil b) Water c) Air d) Paper 

Q21 . Electric potential is a ---------------- a) Vector quantity b) Scalar quantity c) Dimensionless quantity d) None of the above 

Q22 . Which of the following is the good conductor of electricity ? a) Paper b) Iron c) Glass d) Ebonite 

Q23. Concave lens produces ----------- a) only virtual image b) only erect image c) only diminished image d) virtual erect and diminished image 

Q24. The laws of reflection are valid for ----------- a) a convex mirror b) a plane miror c) a concave mirror d) all mirrors irrespective of their shapes 

Q25. Twinkling of stars is due to which optical phenomenon ? a) Reflection b) Interference c) Refraction d) Divergence 

Section –B 

Answer the following question with few words ; 2 x 6 = 12 

Q26. A pencil when dipped in water in aglass tumbler appears to be bent at the interface of air and water . Why ? 

Q27. How is the refractive index of a medium related to the speed of light ? 

Q28. Refractive index of diamond with respect to glass is 1.6 and absolute refractive index of glass is 1.5 . Find the absolute refractive index of diamond ? 

Q29. Should the resistance of an ammeter be low or high ? Give reason . 

Q30 .How does use of a fuse wire protect electrical appliances ? 

Q32. Why is parallel arrangement used in domestic wiring ? 

Section – C 

Answer the following questions : 3 x 6 = 18 

Q 33 . State Ohm’s law ? Does it hold good under all conditions ? 

Q34. What is Joule’s heating effect ? Stae the related laws . 

Q35 . What does the direction of thumb indicate in the right hand thumb rule . In what way this rule is different from Fleming’s left hand rule ? 

Q36. What is the difference between a direct current and an alternating current ? How many times does AC used in India change direction in one second ? 

Q37 .Explain the phenomenon of dispersion of white light through a glass prism , use suitable ray diagram . 

Q38 . How are power and focal length of a lens related ? You are provided with two lenses of focal length 20 cm. And 40 cm respectively . Which lens you use to obtain more convergent rays ? 

Section – D 

The following questions from Q 39 to Q 43 are Assertion (A) , and Reason(R) type question . You have to choose one of the four alternative as correct answer . 1x 5 = 5 

a) Both A and R are true R is the correct explanation of A 

b) Both A and R are true but R is not the correct explanation of A 

c) A is true but R is false 

d) A is false but R is true 

Q39 . Assertion (A) : A ray passing through the centre of curvature of a concave mirror after reflection, is reflected back along the same path.

Reason (R) : The incident rays fall on the mirror along the normal to the reflecting surface.

Q40 . Assertion(A) : The emergent ray is parallel to the direction of the incident ray.

Reason (R) : The extent of bending of the ray of light at the opposite parallel faces (air- glass interface and glass-air interface) of the rectangular glass slab is equal and opposite.

Q41. Assertion (A) : If a graph is plotted between the potential difference and the current flowing, the graph is a straight line passing through the origin.

Reason (R) : The current is directly proportional to the potential difference.

Q42. Assertion (A) : Longer wires have greater resistance and the smaller wires have lesser resistance.

Reason (R) : Resistance is inversely proportional to the length of the wire.

Q43. Assertion(A): The magnitude of the magnetic field at a point on the axis of a current carrying solenoid is inversely proportional to the current flowing through the solenoid.

Reason (R) : The magnitude of the magnetic field at a point on the axis of a current carrying solenoid is directly proportional to the number of turns per unit length of a solenoid.

Section E  

Read the following passage and answer the questions below : 1 x 5 = 5 

The lenses forms different types of images when object placed at different locations. When a ray is incident parallel to the principal axis, then after refraction, it passes through the focus or appears to come from the focus.

When a ray goes through the optical centre of the lens, it passes without any deviation. If the object is placed between focus and optical center of the convex lens, erect and magnified image is formed.

As the object is brought closer to the convex lens from infinity to focus, the image moves away from the convex lens from focus to infinity. Also the size of image goes on increasing and the image is always real and inverted .

A concave lens always gives a virtual, erect and diminished image irrespective to the position of the object.

i) The location of image formed by a convex lens when the object is placed at infinity is a) at focus b) at 2 F c) at optical centre d) between F and 2 F 

ii) When the object is placed at the focus of concave lens, the image formed is a) real and smaller b) virtual and inverted c) virtual and smaller d) real and erect 

iii) The size of image formed by a convex lens when the object is placed at the focus of convex lens is a) small b) point in size c) highly magnified d) same as that of object 

iv) When the object is placed at 2F in front of convex lens, the location of image is

    a) at F b) at 2 F on the other side c) at infinity d) between F and optical center

       V) At which location of object in front of concave lens, the image between focus and optical centre is formed a) anywhere between centre and infinity b) at F c) at 2 F d) infinity 

Section – F 

Answer the following question : 5 x7 = 35 

Q44. The image formed by a concave mirror is observed to be virtual, erect and larger than the object. Where should the position of the object be relative to the mirror? Draw ray diagram to justify your answer.

Q45. The image of a candle flame placed at a distance of 30 cm from a mirror is formed on a screen placed in front of the mirror at a distance of 60 cm from its pole. What is the nature of the mirror? Find its focal length. If the height of the flame is 2.4 cm, find the height of its image. State whether the image formed is erect or inverted.

Q46 a) Define the following terms in the context of spherical mirrors:

 (i) Pole

 (ii) Centre of curvature

 (iii) Principal axis

 (iv) Principal focus

 V) Draw ray diagrams to show the principal focus of a Concave mirror

Q47 List the factors on resistance of a conductor depends . Why are metals are good conductor of electricity whereas glass is a bad conductor ? Give reason . Why are alloys are used in heating instruments ? 

Q48 . A copper wire has diameter 0.5 mm and resistivity 1.6 × 10-8 Ω m. Calculate the length of this wire to make it resistance 100 Ω. How much does the resistance change if the diameter is doubled without changing its length? 

Q49. What is a solenoid? Draw a diagram to show field lines of the magnetic field through and around a current carrying solenoid. State the use of magnetic field produced inside a solenoid. List two properties of magnetic lines of force

Q50 . What is myopia (near-sightedness)? Draw a ray diagram to show how it can be corrected using a lens. 

CBSE question XI

Sub: Physics Class- XI F.M - 100 

Section – A 

Choose the correct alternative (MCQ) 

Q1. The atmospheric pressure is 106 dyne/cm2. What is its value in SI unit? 

a) 10^5newton/m2 (b) 10^6 newton/m2 (c) 10^4newton/m2 (d) 10^3 newton/m2 

Q2. Which of the following groups have different dimensions? 

a) Potential difference, EMF, voltage (b) Pressure, stress, Youngs modulus (c) Heat, energy, work done (d) Dipole moment, electric flux, electric field 

Q3. Which of the following is a dimensional constant? 

a) Gravitational constant (b) Dielectric constant (c) Refractive index (d) Relative density 

Q4. Two trains of 40 m length are travelling in opposite directions with a velocity of 10 m/s and 15 m/s. What is the time of crossing? 

a) 1 s b) 2.4 s c) 3.2 s d) 4.4 s 

Q5. A particle is moving with a constant speed along a straight-line path. A force is not required to : a) change its direction b) decrease its speed c) keep it moving with uniform velocity d) Increase its momentum

Q6. Which theorem states that “If a particle under the simultaneous action of three forces is in equilibrium, then each force has a constant ratio with the sine of the angle between the other two forces”? a) Lay’s theorem b) Lami’s Theorem c) Newton’s law d) Faraday’s theorem

Q7. Give an example of motion in two dimensions _________________ a) Motion along a straight line in any direction b) Bird flying c) A flying kite d) Projectile motion 

Q8. Circular motion is a _________________ a) Motion in one dimension b) Motion in two dimensions c) Motion in three dimensions d) Motion in four dimensions

Q9. Which is the branch of physics that deals with the motion of a body by considering the cause? a) Statics b) Thermodynamics c) Dynamics d) Astronomy

Q10. When an external force is not applied to the system, its total momentum _____________ a) Becomes zero b) Remains constant c) Increases gradually d) Decreases gradually

Q11. Forces acting for a short duration are called _____________ a) Short force b) Interval force c) Impulsive forces d) Interrupting force

Q12. The inherent property, with which a body resists any change in its state of motion is known as _____________ a) Force b) Momentum c) Inertia d) Acceleration 

Q13. Which is the type of collision in which both the linear momentum and the kinetic energy of the system remain conserved? a) Inelastic Collision b) Elastic Collision c) Destructive collision d) None of the options 

Q14. State true or false: According to Equivalence of Mass and Energy, it states that mass and energy are NOT interconvertible. a) True b) False 

Q15. An electric heater of rating 1000 W is used for 5 hrs per day for 20 days. What is the electrical energy utilized? a) 100 kWh b) 200 kWh c) 120 kWh d) 500 kWh 

Q16. Find the potential energy stored in a ball of mass 5 kg placed at a height of 3 m above the ground. a) 121.20 J b) 147.15 J c) 227.31 J d) 182.21 J 

Q17. The rotational inertia of a rigid body is referred to as its _________________. a) Moment of energy b) Moment of force c)Moment of inertia d) Moment of acceleration 

Q18. If a body is rotating about an axis passing through its centre of mass, the angular momentum of the body is directed along its _________________. a) Circumference b) Radius c) Axis of rotation d) None of the option 

Q19 . The combination of rotational motion and the translational motion of a rigid body is known as _________________. a) Frictional motion b) Axis motion c) Angular motion d) Rolling motion

Q20. State true or false: The position of centre of mass does not depend upon the shape, size, and distribution of the mass of the body. a) True b) False 

Q21. The sum of kinetic and potential energy is when a missile is launched with a velocity less than the escape velocity. a) 0 b) Negative c) Positive d) None of these options 

Q22. What would be the maximum height reached by the body if the body is projected vertically from the surface of the earth of radius R with a velocity equal to half of the escape velocity? a) 2 + R b) R c) R/2 d) R/3  

Q23. The satellite having the same time period of revolution as that of the earth is called _________________. a) Stationary satellite b) Geostationary satellite c) Gravitational satellite d) Geo satellite 

Q24. State true or false: The gravitational force is a conservative force. a) True b) False

Q25. Which one has higher kinetic energy? Both light and heavy bodies have equal momenta. a)Heavy body b) Light body c) Both d) None of the options

Section – B 

Answer the following questions with few words : 2 x 6 = 12 

Q26. Why the moment of inertia of a solid disc is smaller than that of a ring of same size and mass? 

Q27. Name the process in which (i) momentum is conserved but K.E. is not conserved and (ii) momentum changes but K.E. does not change.

Q28. Two objects having different masses have same momentum. Which one of them will move faster. 

Q29. Can an object be at rest as well as in motion at the same time? 

Q30. Name Physical Quantities Whose Units are Electron Volt and Pascal. 

Q31. What is the shape of the displacement time graph for uniform linear motion?

Section –C 

Answer the questions below briefly : 3x 6 = 18 

Q32. If Velocity, Time and Force Were Chosen as the Base Quantities, Find the Dimensions of Mass. 

Q33. The displacement x of a particle moving in one dimension under the action of the constant force is related to the time by the equation t = x^0.5 -3 where x is in meters and t is in seconds. Find the velocity of the particle at (1) t = 3s (2) t = 6s.

Q34. What is the angle between two forces of 2 N and 3 N having resultant as 4 N?

Q35. Two blocks of masses m1 and m2 are connected by light spring on a smooth horizontal surface. The two masses are pulled apart and then released. Prove that the ratio of their acceleration is inversely proportional to their masses. 

Q36. Four particles of mass , 1kg , 2 kg ,3 kg , and 4kg are placed at the four vertices , , and of square of side . Find the position of centre of mass of the system . 

Q37. Show That an Artificial Satellite Circling Round the Earth in an Orbit of Radius Obeys Kepler’s Third Law.

Section – D 

Directions : 

Each of these questions contain two statements, Assertion and Reason. Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.

(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion

(c) Assertion is correct, reason is incorrect

(d) Assertion is incorrect, reason is correct

Q 38. Assertion : When we change the unit of measurement of a quantity, its numerical value changes.

Reason : Smaller the unit of measurement smaller is its numerical value.

Q39. Assertion : Displacement of a body may be zero when distance travelled by it is not zero.

Reason : The displacement is the longest distance between initial and final position. 

Q40. Assertion : On a rainy day, it is difficult to drive a car or bus at high speed.

Reason : The value of coefficient of friction is lowered due to wetting of the surface.

Q41. Assertion : A man rowing a boat upstream is at rest with respect to the bank. He is doing no external work.

Reason : Work done by constant force, W = F s cosθ. 

Q42. Assertion : A body becomes massless at the centre of earth.

Reason : This follows from g’ = g (1 – d/R) 

Section – E 

Q43. Read the passage below and answer the questions that follow ; 1 x 5 =5 

Conservation of Momentum    

This principle is a consequence of Newton’s second and third laws of motion.

In an isolated system (i.e., a system having no external force), mutual forces (called internal forces) between pairs of particles in the system causes momentum change in individual particles.

Let a bomb be at rest, then its momentum will be zero. If the bomb explodes into two equal parts, then the parts fly off in exactly opposite directions with same speed, so that the total momentum is still zero. Here, no external force is applied on the system of particles (bomb).

(i) A shell of mass 10 kg is moving with a velocity of 10 ms-1 when it blasts and forms two parts of mass 9 kg and 1 kg respectively. If the first mass is stationary, the velocity of the second is (a) 1 m/s (b) 10 m/s (c) 100 m/s (d) 1000 m/s 1

(ii) A bullet of mass 10 g is fired from a gun of mass 1 kg with recoil velocity of gun 5 m/s. The muzzle velocity will be (a) 30 km/min (b) 60 km/min (c) 30 m/s (d) 500 m/s 1

(iii) A bullet of mass 0.1 kg is fired with a speed of 100 m/s. The mass of gun being 50 kg, then the velocity of recoil becomes (a) 0.05 m/s (b) 0.5 m/s (c) 0.1 m/s (d) 0.2 m/s 1

(iv) Two masses of M and 4M are moving with equal kinetic energy. The ratio of their linear momenta is (a) 1:8 (b) 1:4 (c) 1:2 (d) 4:1 2

Answer the following questios : 5 x7 = 35 

Q44. A physical quantity P is related to four observables a, b,c and d and as follows: P = a^3b^2 /(c^.5 d^.5) The percentage errors of measurement in a , b, c and d are 1 and 2 respectively. What is the percentage error in the quantity P? If the value of P calculated using the above relation turns out to be 3.763, to what value should you round off the result?

Q45 . A particle is moving along a straight line and its position is given by the relation x = (t^3 – 6t^2 –15 t + 40 ) m 

Find 

a) The time at which velocity is zero.

b) Position and displacement of the particle at that point.

c) Acceleration

Q46. A man can swim with a speed of 4km/ h in still water. How long does he take to cross a river wide if the river flows steadily at 3km/h and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank? 

Q47. A monkey of mass 4 kg climbs on a rope which can stand a maximum tension 600 N. In which of the following cases will the rope break? The monkey (a) climbs up with an acceleration of 6m/s^2 (b) climbs down with an acceleration of 4m/s^2 (c) climbs up with a uniform seed of 5 ms (d) falls down the rope freely under gravity. Take g = 10m/s^2 and ignore the mass of the rope. 

 Q48. The resistance of certain platinum resistance thermometer is found to be 2.56 ohm at 0 degree celsius and 3.56 ohm at 1000 degree celsius . When the thermometer is immersed in a given liquid, its resistance is observed to 5.06 ohm . Determine the temperature of liquid? 

Q49. A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N ? What is the linear acceleration of the rope? Assume that there is no slipping.

Q50 . A 400 kg satellite in a circular orbit of radius 2 Re about the earth. Calculate the kinetic energy, potential energy and total energy of the satellite. ( Re = 6.4 x 10 ^6 m M = 6x 10^24 kg

Class X question CBSE

Class – X (CBSE) F.M -100 

Section -A 

Choose the correct alternative (MCQ) : 1 x 25 = 25 

1. A convex lens and a concave lens having focal lengths 10 cm and 20 cm respectively are placed in contact with each other . Which of thefollowing statements is correct about the lens combination ? 

A) It will behave likea plane glass slab  

B) It will behave like a convex lens 

C) It will behave like a concave lens 

D) It will behave vlike a cylindrical lens 

2. The part of eye which causes change in the focal length of eye lens to provide it exceptional accommodation power is : 

A) Aqueous humour B) Ciliary muscles C) Pupil D) Iris 

3. Pushkar was studying a light phenomenon and wrote down the following statements in that contex : 

i) A concave mirror can be used as a shaving mirror because it can form an enlarged , virtual image when object is placed between the pole and focus . 

ii) A convex lens always forms real , inverted images , regardless of the position of the object . 

iii) The relationship between object distance (u) , image distance (v) and the focal length (f) of the lens is given by 1/f = 1/v - 1/u 

Choose the option enlisting all the correct statements : 

A) I ) and ii) B) i) and iii) C) ii) and iii) D) I) , II) and iii) 

4. During a lab experiment , Bhavna uses a solenoid connected to a battery . She note down the following facts : 

i) The pattern of the magnetic field lines inside the solenoid is similar to a bar magnet . Ii) The north pole and south pole of the current – carrying solenoid can be identified by applying the right hand rule . Iii) A solenoid can be used to magnetise a piece of a soft iron making it an electromagnet .

Choose the option enlisting all the correct statements : 

A) i) and iii) B) ii) and iii) C) i) and ii) D) i) , ii) and iii) 

5. When a convergent beam of light is incident on a convex mirror , the reflected rays appear to be coming from 20cm behind the mirror and retrace their path . The focal length of the mirror is 

A) 20 cm B) 10 cm C) 40 cm D) 30 cm 

 

6. In the above diagram the values of bthe angle of incidence and the angle of reflection are : 

A) I = 50 ° , r = 40° B) i = 40° , r = 50° C) i = 40° r = 40° D) I = 50° r = 50° 

7. An object is placed at a distance of 0.25 m in front of a plane mirror . The distance between the object and image will be – A) 0.25 m B) 1.0 m C) 0.5 m D) 0.125 m 

8. An object at a distance of 30 cm from a concave mirror gets its image at the same point . The focal length of the mirror is A) - 30 cm B) 30 cm C) - 15 cm D) 15 cm 

9. The least resistance obtained by using 2 Ω , 4 Ω , 1 Ω and 100 Ω is 

 A) < 100 Ω B) < 4 Ω C) < 1 Ω D) > 2 Ω 

10. Work of 14 J is done to move 2 C charge between two points on a conducting wire . What is the potential difference between the two points ? 

A) 28 V B) 14 V C) 7 V D) 3.5 V 

11. Electrical resistivity of a given metallic wire depends upon - 

A) its length B) its thickness C) its shape D) Nature of the material 

12. What is the relationship between resistance and current ? 

A) They are directly related to each other 

B) They are inversely related to each other 

C) The resistance has a greater magnitude than the current 

D) The current has a greater magnitude than the resistance 

13. Which of the following represents voltage ? 

A) Work done / Current x time B) work done x Charge C) Work done x time / Current D) Work done x Charge x Time 

14. A coil in the heater consumes power P on passing current . If it is cut into halves and joined in parallel , it will consume power A) P B) P/2 C) 2P D) 4P 

15. The most suitable material for making the core of an electromagnet is : 

A) Steel B) Iron C) Soft Iron D) Aluminium 

16. When a staright conductor is carrying current : 

A) There are circular magnetic field lines around it 

B) There are magnetic field lines parallel to the conductor 

C) There are no magnetic field lines 

D) None of the above 

17. The magnetic field lines inside a straight solenoid carrying current : 

A) is zero B) Decrease as we move towards its end C) Is the same at all points D) Increase as we move towards its end 

18. The force on a current carrying conductor when placed perpendicular in a uniform magnetic field . A) F = BIL B) F = B/IL C) F = L/BI D) F = I/BL

19. A soft iron bar is introduced inside a current-carrying solenoid . The magnetic field inside a solenoid : A) Decrease B) Will increase C) Will become zero D) Will remain unaffected 

20. In which part of the human eye is the image of an object formed ? 

A) Iris B) Pupil C) Retina D) Cornea 

21. The splitting of white light into different colours on passing through a prism is called A) Reflection B) Refraction C) Dispersion D) deviation 

22. What lens is used to correct myopia (short-sightedness )? 

A) Convex lens B) Concave lens C) Bifocal lens D) Cylindrical lens 

23. Which colour bends the most when white light passes through a glass prism ? 

A) Red B) Yellow C) Violet D) Green 

24. Why does the clear sky appear blue ? 

A) Blue light absorbed by the atmosphere B) Blue light scatters the most C) Red light scatters the most D) Ocean water reflect blue light 

25. The danger signals installed at the top of tall buildings are red in colour . This can be easily seen from a distance because among other colours , the red light 

A) is scattered the most by smoke or fog 

B) is scattered the least by smoke or fog 

C) is absorbed the most by smoke or fog 

D) moves faster in the air 

Section – B 

From Q 26 to Q 31 carries 2 mark each ( 2x 6 =12 ) and from Q32 to Q37 carries 3 mark each ( 3x 6 = 18) 

26. What is the magnification of images formed by plane mirrors and why ? 2 

27. Draw a labelled ray diagram to show the path of the reflected ray corresponding to an incident ray of light parallel to the principal axis of a convex mirror . Mark the angle of incidence and angle of reflection . 2 

28. state Ohms law and explain . 2 

29. List three factors on which the resistance of a conductor depends . 2 

30. If the field lines of a magnetic field are crossed at a point , what does it indicate ? 2 

31. List the two causes of hypermetropia . 2 

32 .What eye defect is myopia ? Describe with neat diagram how this defect of vision can be corrected by suitable lens . 3 

33. List two possible ways in which a concave mirror can produce a magnified image of an object placed in front of it . State the difference if any between these two images . 3 

34. The absolute refractive indices of glass and water are 4/3 and 3/2 respectively . If the speed of light in glass is 2 x 10^8 m/s , calculate the speed of light in vacuum , water . 3 

35. Calculate the resistivity of the material of a wire of length 1.0 m ,radius 0.01 cm and resistance 20 ohms . 3 

36. State the three factors on which the strength of magnetic field mproduced by a current carrying solenoid depends . 3 

37. Write about power of accommodation of human eye . Explain why the image distance in the eye does not change when we change the distance of an object from the eye ? 3 

Section – C 

Following questions( Q38 to Q42) consist of two statements – Assertion(A) and Reason (R) . Answer these questions selecting the appropriate option given below : 

a) Both A and R are true and R is the correct explanation of A 

b) Both A and R are true but R is not the correct explanation of A 

c) A is true but R is false 

d) A is false but R is true 

38. Asserion (A) : The emergent ray is parallel to the direction of the incident ray .

Reason (R) : The extent of bending of the ray of light at the opposite parallel faces ( air-glass interface and glass-air interface ) of the rectangular glass slab is equal and opposite . 1 

39. Assertion(A) : Light travels faster in glass than in air .

Reason (R) : Glass is denser than air . 1 

40. Assertion (A) : A current–carrying wire does not get electrically charged .

Reason(R) : The electric current in a metal wire is due to the flow of free electrons , where the total number of protons in the wire is equal to the total number of electrons . 1 

41. Assertion( A) : If a graph is plotted between the potential difference and the current flowing . 

Reason( R) : The current is directly proportional to the potential difference . 1 

42 . Assertion(A) : As the speed of the coil in the motor increases , there is a reduction in the current flowing through it . 

Reason (R) : During rotation in an electric motor , some induced current is produced. 1

Section –D 

Read the passage and the questions that follow : 5 

43 . An electric iron is a home appliance that uses electricity to produce heat . Inside iron , there is a heating element made of a high – resistance material like nichrome wire . When a voltage( V) is applied across the ends of this wire , an electric current (I) flows through it . The rate at which electrical energy is used up is called electric power (P) .A typical household electric iron has a rating of 1000 W , 220V stamped on it , meaning it consumes 1000 joules of energy every second when connected to a 220 V supply . 

i) What is the meaning of the rating 1000 W , 220V on an electric appliance ? 1 

ii) Calculate the electric current (I) flowing through the iron when it is connected to the 220 V mains . 1

iii) Find the resistance (R) of the heating element on the electric iron . 1 

iv) How much electrical energy( in kWh) is consumed if the electric iron is used for 2 hours daily over a period of 30 days ? 2 

Section – E 

This section has 7 questions with 5 marks for each question .

44. A convex lens has a focal length of 10 cm . At what distance from the lens should the object be placed so that it forms a real and inverted image 20 cm. Away from the lens ? What would be the size of the image formed if the object is 2 cm high ? With the help of a ray diagram show the formation of the image by the lens in this case ? 5  

45 . Draw a ray diagram to show the use of a convex lens for the formation of images having the following characteristics .  

a) Real and inverted and diminished b) Virtual , erect & magnified 5 

46. Explain parallel combination of resistors and derive the formula for equivalent resistance . 5

47. A) Write the mathematical expression for Joules law of heating . B) Compute the heat generated while transferring 96000 coulomb of charge in two hours through a potential difference of 40 V . 5

48. Make a diagram to show how hypermetropia is corrected . The near point of a hypermetropic eye is 1 m . What is the power of the lens required to correct this defect ? Assume the near point of the normal eye is 25 cm . 5

49. Explain the principle , construction and working of an electric motor with the help of a leveled diagram . 5

50 .Differentiate between refraction , dispersion and scattering of light with specific o example for each phenomenon . 5

Class XI question paper CBSE

 

1.      The pair having the same dimensions is  a) Angular momentum , work  b) Work, torque  c) Potential energy  , linear momentum  d) Kinetic energy , velocity

2.      Which one has the dimension different from the remaining three  a) Power b) Work c) Torque d) Energy

3.      Torr is the unit of  a) Pressure b) Volume c) Density d) Flux

4.      Which one is a vector : a) Length b) Volume c) Velocity d) Work

5.      The magnitude of the vector 2/3 i –1/3 j + 2/3 k is : a) Zero b) One  c) Three d) 1/9

6.      If the x- component of a vector is positive and y- component is negative , then resultant vector lies in what quadrant : a) 1^st quadrant  b) 2^nd quadrant  c) 3^rd quadrant  d) 4^th quadrant

7.      Slope of velocity time graph is : a) Acceleration b) Distance  c) Force  d) Momentum

8.      Which law of motion is also called law of inertia ? a) 1 st law b) 2 nd law c) 3^rd law  d) 4^th law

9.      Momentum depends on a) Force acting on the body b) Mass of the body  c) Velocity of the body  d) Both mass and velocity of the body

10.  Area under the curve of force-displacement graph is equal to : a) Displacement b) Work  c) Power  d) Energy

11.  When a force is parallel to the direction of motion of the body , then work done on the body  is : a) zero b) minimum  c) infinity  d) Maximum

12.  Power is also defined as dot product of a) Force and displacement  b) Force and mass  c) Force and velocity  d) Force and time

13.  Moment of inertia is equal to : a) m^2 r  b) m^2 r^2  c) m r  d) m r^2

14.  The rate of change of angular displacement is called :  a) Angular displacement  b) Angular velocity  c) Angular acceleration  d) Torque

       15.  Centripetal force performs  a) Maximum work  b) Minimum work c) Negative work  d) no work

      16. When torque acting on system is zero , which of the following will be constant : a) Linear momentum  b) Force c) Angular momentum  d) impulse

     17. Geo-stationary satellite completes one rotation around earth is : a) 3 hours b) 6 hours c) 12 hours d) 24 hours

18. If a body of mass 10 kg is allowed to fall freely , its weight becomes a) zero  b) 98 N c) 9.8 N d) 10 N

19. The apparent weight of a man in an ascending lift moving with acceleration ‘a’  a) Increases  b) decreases c) Remains constant  d) Becomes zero

20. A particle is moving in a circle with constant speed . The direction of centripetal force will be  a) Along tangent  b) Along radius towards center c) Along radius away from center  d) Changing with motion

21. The escape velocity from the earth surface  in km/s  is : a) 4.2 km/s  b) 7.5 km/s c) 9.5 km/s d) 11 km/s

22. Motion of projectile is ---------- dimensional  a) One  b) Two  c) Three  d) Four

23. Inertia of an object is quantitative measure of its : a) Volume b) Density  c) Mass  d) Temperature

24. When velocity time graph is a straight line parallel to the time axis then : a) Acceleration is const  b) Acceleration is variable  c) Acceleration is zero  d) Velocity is zero

25 . The direction of torque can be found by : a) Head and tail rule  b) Right hand rule  c) Left hand rule  d) Fleming rule

Section – B

Answer the following questions with few words : 2 x 6 = 12

26. Define S.I unit of solid angle .

27. What is the relative velocity of two bodies having equal velocities ?

28.Two vectors  A and B are perpendicular to each other . What is the value of A.B  ?

29.When an air buble rises in water , what happens to its potential energy ?

30. A wheel 0.5 m in radius is moving with a speed of  12m/s . Find its angular speed .

31. Why is gravitational potential energy always negative ?

Answer the following questions briefly .  3 x 6 = 18

32. At what height above the surface of the earth , the value of acceleration due to gravity is  reduced to one fourth of its value on the surface of earth ?

33.Find the dimension of latent heat and specific heat .

34. A particle is thrown upwards . It attains a height (h) after 5 seconds and again after 9 s comes back . What is the speedof the particle at height h ?

 

 

35. Prove that the centre of mass of two particles divides the line joining the particles in the inverse of their masses .

36. Find the radius of gyration of a solid sphere about its diameter .

37 . A thief jumps from the roof of a house with a box of weight W on his head. What will be the weight of the box as experienced by the thief during jump?

Section – C

Directions: Each of these questions contain two statements, Assertion and Reason. Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.

(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion

(c) Assertion is correct, reason is incorrect

(d) Assertion is incorrect, reason is correct.  1 x 5 = 5

38. Assertion: A body loses weight when it is at the centre of the  earth.

Reason: At the centre of earth, g = 0. Therefore, weight = mg = 0.

39. Assertion : If earth suddenly stops rotating about its axis, then the value of acceleration due to gravity will become same at all the places.

Reason : The value of acceleration due to gravity depends upon the rotation of the earth.

40. Assertion : Gravitational force between two particles is negligibly small compared to the electrical force.

Reason : The electrical force is experienced by charged particles only.

41. Assertion : The centre of mass of a body may lie where there is no mass.

Reason : Centre of mass of body is a point, where the whole mass of the body is supposed to be concentrated.

42. Assertion : Two particles of different mass, projected with same velocity at same angles. The maximum height attained by both the particle will be same.

Reason : The maximum height of projectile is independent of particle mass.

Section – D

43.  Read the passage below answer the questions that follow :       1x 5 = 5

Kinematics is the branch of mechanics which deals with the study of motion of material

objects without taking into account the factors affecting the motion. Rest and motion are

relative concept and nothing is absolute. The Position of the object at a given instant of time

is described in terms of position coordinates. The coordinate system along with a clock

constitutes a frame of reference. Frame of reference can be of two types viz: inertial frame of

reference and non-inertial frame of reference. When position of body change in a frame of

reference, it is said to be in motion which is categorised as uniform and non-uniform. Motion

of a body is studied in terms of position-time graph and velocity-time graph.

(i) "Rest and motion are relative not absolute." Comment.

(ii) What are different types of frames of reference? Explain.

(iii) Draw position-time graph for uniform and Non-uniform motion.

(iv) Draw velocity-time graph for uniform and non-uniform motion.

(v) Relative veolcity of two bodies is zero. What is nature of Position-time graph for it?

 

 

 

 

Section – E

Answer the following questions : 5 x7 = 35

44.  The unit of length convenient on the nuclear scale is a feri : 1 f = 10^-15 m . Nuclear sizes objects roughly obey the following empirical relation : r = r° A^1/3 , r is the radius of the nucleus , A its mass number r° is a constant equal to 1.2 f . Show that the rule implies that nuclear mass density is nearly constant for different nuclei .

45. A balloon is ascending at the rate of 4.9m/s. A pocket is dropped from the balloon when situated at a height of 245m. How long does it take the packet to reach the ground? What is its final velocity?

46. A particle starts from the origin at t = 0 s  with a velocity of 10j m/s  and moves in the x-y plane with a constant acceleration of  (8i + 2j) m/s^2

a) At what time is the x-coordinate of the particle  16 m ? What is the y-coordinate of the particle at that time?

47. Why is horizontal velocity constant in projectile motion? Why are two projection angles possible for the same range?

48. If speed doubles, what happens to kinetic energy? If the same bullet emerges with 10% of its initial kinetic energy, find its speed.

49. What is the relation between linear velocity and angular velocity? Why do particles on the axis of rotation remain stationary?

50. Why is g maximum at Earth’s surface?

Wave Optics

Introduction : 

In 1637;Descattes gave cospuscular theory of light and derived Snell's law . The cospuscular theory predicted that if a ray of light bends towards the normal the speed of light in the second medium would be greater than the first medium .Corpuscular theory was further developed by Newton . In 1678, the Dutch physicist Christian Huygens put forward the wave theory of light .It predicted that if light bends towards the normal its speed in second medium would be less than the first , a sharp contrast to the Corpuscular theory .In 1850, Foucault experimentally proved that speed of light in water is less than speed in air confirming the wave nature of light . Wave theory was not firstly accepted because of great authority of Newton . However Thomas Young in 1801 performed his famous interference experiment firmly establishing the wave theory .

The phenomena of interference , diffraction ,reflection and refraction are well explained by the wave model of light . The only difficulty is that for a wave to propage a medium is needed. But light can travel in vaccum also . This was explained by Maxwell when he proved the electromagnetic nature of light .Maxwell developed a wave equation by assuming light is a propagation electric and magnetic vector mutually perpendicular to each other.From this he calculated the speed of light in vacuum . Value so obtained is very close to the experimentally obtained value of speed of light . So he confirmed light as electromagnetic wave able to propagate on free space .Light waves are associated with changing electric and magnetic field .Changing electric field produces time and space varying magnetic field and changing magnetic field produces time and space varying electric field .The changing electric and magnetic field result in propagation of electromagnetic waves in vacuum .

Huygens Principle : 

When we drop a small stone on the surface of calm pond ,waves are generated and spread out from the point of impact .Waves are seen as circular ring spreading out from point of origin . All points on such a circle are oscillating in phase because there are at same distance from the source . So locus of all points oscillating in phase is called wave front . A wave front is defined as surface of constant phase .The speed with which the wavefront moves outwards from the source is called speed of the wave . The energy of the wave travels in a direction perpendicular to the wave front . If the wave front is a sphere then it is called spherical wavefront . At a large distance a portion of the sphere can be considered as plane and we get plane wave front .

If we know the shape of wavefront at a time t= 0 we can construct the wave front at later time using Huygens principle .It is essentially a geometrical construction. According to Huygens principle , each point on the wavefront is the source of secondary waves and the  secondary wavelets generating from these points spread out in all directions with the speed of the wave .If we draw a common tangent to all these spheres we get the position of wavefront at later time .

If we want to draw the shape of wavefront at time t , we draw spheres with radius vt  at each point on the wavefront( t =0) and if we draw a common tangent to all the spheres we get spherical wavefront at time t .The new wavefront G1G2 is again a spherical wavefront. The above model has a short coming , there is a backward wave .Huygens argued that amplitude of backward wave is zero .

With use of Huygens principle we can construct plane wavefronts also 

Refraction of a plane wave : 

We can derive laws of refraction using Huygens principle .

We will now use Huygens principle to derive laws of refraction.Let v1 and v2  are the speed of light in medium 1 and 2 respectively.We assume a plane wavefront A'A incident on the interface at an angle I as shown in the figure. Let t be the time taken by the wavefront to travel the distance BC . Thus BC= v1t . In order to determine the shape of refracted wavefront we draw a sphere of radius v2t  from the point A .Let CE represent a tangent plane drawn from point C to the sphere . Then AE = v2 t and CE is the refracted wave front . From the triangle ABC and AEC we readily get , 

Sin i = BC/AC = v1t/AC 

Sin r = AE/AC = v2t/AC , where i and r are the angle of incidence and refraction respectively . From the above relations we get ,

Sin I/Sin r = v1/v2 

From the above relation we get the result , if i > r then then v2< v1 implies if velocity is less in second medium rays bend towards the normal . If experimentally proved contrasting the corpuscular theory of light . Now , n1 = C/v1 ( n1 is the refractive index of first medium) Similarly for the 2nd medium 

n2 = C/v2  So

 n2/n1 = v1/v2

Giving Sin i /Sinr = n2/n1

Or , n1 Sin i = n2 Sin r , this is Snell's law of refraction.

If we take BC = one  wavelength in medium 1(lamda1) then AE will also be one wave length(lamda2) in medium 2 

So v1/v2 = lamda1 /lamda2

This implies v1/lamda1 = v2/lamda2

Gives the frequency is same in both the media .

So when light travels from one to another medium its wavelength is changed but not its frequency .

Reflection of a plane wave front by a plane surfac : 

We consider a plane wavefront AB incident at an angle I on a reflecting surfac MN . If v represents the speed of light and t is the time of taken by the  wavefront to reach from B to C then the distanc BC = v t In order to construct the reflected wavefront  we draw a circle with radius v t  from the point A . CE represents the tangent to the circle from C . Obviously AE = BC = v t 

. The triangle AEC and ABC  are congruent.Therefore i = r . This is law of reflection.

With the laws of reflection and refraction we can understand behaviour of lenses ,prism and mirror . When a plane wavefront passes through a thin prism emergent wavefront remain plane with a tilt as shown in the figure .But a plane wavefront passing through a lens it becomes spherical with radius equal to focal length and when reflected by a concave mirror it also becomes spherical wavefront with radius R/2 .

Coherent and Incoherent Addition of waves : 

Here we will discuss about interference pattern produced by superposition of two waves . The superposition principle :At a particular point in a medium the resultant displacement produced by a number of waves is the vector sum of displacements produced by each of the waves . 

We consider two niddles on the surface of water moving up and down periodically and identically .They produce two  water waves and at a particular point the phase difference produced by the two waves remain constant . When this happen we say the sources are coherent .We consider the points where S1P = S2P .Since the distances of the point P is same from both the points The two waves will reach the point P at the same times . So  the two displacement can be represented by ,

y1 = a cos wt  

and  y2 = a cos wt 

So the resultant displacement y is ,

y = y1 + y2 = 2a cos wt , so the resultant intensity is given by ,

I = 4 Io , Io is the intensity produced by individual waves and it is proportional to a^2 , amplitude square . Here the two waves interfere constructively and what we call it as constructive interference .

If the path difference at point P of waves coming from the two sources is 2 x wave length then the the waves can be written as

 y1 = a cos wt 

and y2 = a cos (wt - 4 pi)= a cos wt  , where path difference of 2 x wave length implies a phase difference of 4 pi . The two waves are once again in phase so the resultant intensity is 4 Io giving constructive interference .

But if the path difference is 2.5 x wavelength then the waves may be written as y1 = a cos wt and

y2 = a cos ( wt + 5 pi) = - a cos wt 

The two waves are out of phase calcelling each other giving intensity zero. Here the waves interfere destructively .

To summarise: If we have two coherent sources S1 and S2 vibrating in phase and for arbitrary point P where the path difference, 

S1P - S2P = n x lamda ( n = 0 , 1 ,2, 3 .......) we will have constructive interference  and the resulttant intensity will be 4 Io .

On the otherhand if the path difference at P is (n+1/2) multiple of wavelength i.e 

S1P - S2P = ( n +1/2)x lamda  ( n =0,  1 , 2 , 3 ........) then the waves will interfere destructively giving intensity zero at the point P.

For any arbitrary point G let the difference between two waves is ዋ .The can be represented by ,

y1 = a cos ω t and y2 = a cos( ധt + φ)

And the resultant displacement is given by , 

y = y1 + y2 

    = a [ cos ωt + cos( ω t + φ) 

    = 2 a cos( φ /2) cos ( ω t + φ/2)

The amplitude is given by 2 a cos (φ/2) and therefore intensity is given by 

I = 4 Io cos^2( φ/2) 

If  φ = 0 , 土 2π ,土4 π,  ........

We have constructive interference.

On the other hand if 

φ = 土 π, 土 3 π, 土 5 π .... We have destructive interference leading to zero intensity .

Now if the two sources are coherent the phsase difference fi will not change with time at any  point i.e maxima and minima will not change with time and we will get stable interference pattern . If the phase difference of the two sources changes rapidly with time we say the sources are incoherent. This is what happens when two separate sources illumanate a wall .

geometrical optics

Introduction: 

Electromagnetic radiation belonging to the wave length range between 400 nm to 800 nm is called light . It travels with an enormous speed in straight line in vacuum . It's speed in vacuum is 3 x 10^8 m/s . It's speed in vacuum  is the highest speed attainable in nature . A light wave can be considered to travel from one point to another in a  straight line joining them . Such a path of light is called ray of light . A bundle of light rays is called a beam of light .We will discuss the phenomena of reflection refraction and dispersion of light using ray picture. Next we understand some optical instruments such as microscope , telescope and human eye using the ray property of light .

Reflection on spherical surface : 

We know the laws of reflection : 1) Incident ray , reflected ray and normal on  the reflecting surface at the point of incident all lie in the same plane .2) Angle of incident ( angle between incident ray and normal ) and angle of reflection ( angle between reflected ray and normal ) are equal to each other . These laws are valid in all reflecting surfaces whether it is plane or curved .In curved surface normal is drawn on the tangent at the incident point  and it passes through the centre of curvature of the curved surface. Centre of curvature is the centre point of the sphere forming the curved mirror .

The geometric centre of a spherical mirror is called its pole . In case of lens it is called optical centre.The line joining between pole and centre of curvature is called principal axis . In case of lens principal axis is the line joining between optical centre and principal focus .

Sign convention: 

In Cartesian sign convention here pole is taken as origin and the distances measured in the direction of light rays are taken as positive and the direction measured against the light rays is taken negative . The distance upward to principal axis is taken positive and the downward to the principal axis is assumed negative . 

Focul length of spherical mirror: 

Light rays travelling parallel to the principal axis after reflection from spherical  mirror converge to a point on the principal axis for concave mirror and for convex mirror light rays appears to diverge from a point on the principal axis . This point on the principal axis is called Principal focus . The distance between the pole and focal point is called focal length of the mirror.

Focal length is denoted by f and radius of curvature is R . Let us derive the relation between them . 

Let a light ray parallel to the principal axis incident on M .After incident on it reflects and passes through the point F on the principal axis . The normal at M passes through the centre of curvature C .Let MD is perpendicular drawn on principal axis . Since the angle of incidence is equal to angle of reflection from the triangle CMD  we get MD/CD = tan(theta) .and triangle FMD,  MD/FD = tan(2theta) Since angle theta is small we can write  theta = MD/CD and 2 theta = MD/FD . From these relation we get 2 MD/CD = MD/FD Or CD = 2FD . D is very close to O . so we ca write CO = 2OF or R = 2 f 

The mirror equation : 

If rays emanating from a point actually meet at another point after reflection or refraction then that point is called the image of the first point .The image is real if the rays converge to the point and image is virtual if rays appear to diverge from the point . 

In principle any two rays emanating from a point find their point of intersection and thus get the image of the point due to reflection from a spherical mirror . To draw the image it is convenient to follow any of the two procedures from the following.

i) The ray from the point coming para to the principal axis after reflection goes through the focus of the mirror.

ii) The ray passing through the centre of curvature of the concave mirror retraces back to its path after reflection.

iii) Any ray passing through the focus of the mirror becomes parallel to the principal axis after reflection.

iv) The ray incident at any angle at the pole is reflected following the law of reflection.

Figure shows the rays diagram for the above  three rays . Here AB is image and A'B' is real image .The two right angled triangles A'B'F and MPF are similar .Therefore,

A'B'/PM = B'F/PF ( MP is considered perpendicular to principal axis for small mirror) 

Or A'B'/AB = B'F/PF ( PM = AB)

Since  angle APB' = angle A'PB so triangle ABP and A'PB' are similar .

Hence 

AB/A'B' = PB/PB'  

From the above two relations we get ,

B'F/PF = PB'/PB 

Or, (B'P - FP)/PF = PB'/PB

Or ,( - v + f )/-f  = - v/-u 

When simplified we get 

1/v + 1/u = 1/f 

This is known as mirror equation.

Magnification : 

It is defined as the ratio of image height and the object height= A'B' / AB = h'/h  From the above relation we get A'B'/ AB = PB'/PB = v/u 

So magnification, m = -h'/h = -v/u ( image is inverted so the negative sign ) 

REFRACTION : 

When a light rays travelling from one medium incidents obliquely on the interface of another medium a part of the light ray transmit with direction changed  at the interface of two medium . It is called refraction of light . Snell experimentally obtained the following two laws of refraction .

I) The incident ray reflected rays and the normal to the interface at the point of incidence all lie in the same plane .

II) The ratio of sine of angle of incidence to the sine of angle of refraction is constant for a given pair of media and for a given colour of light .

We have  sini/son r = n21, where n21 is a constant and called the refractive index of medium 2 with respect to medium 1 .It is Snall's law of refraction. If n21 is greater than 1 then medium 2 is optically deser medium .If n21 is less than unity theefium two is rarer medium . If n21 > 1 then  i > r reverse is the case if  n21<1 . Optical density bshould not be confused with mass density. Optical density may be greater where mass density is lower . In case of water and terpenpine oil .mass density of water is greater than terpentine oil. But optical density of terpentine oil is greater than water .

Since the path of light is reversible, n21 = n12 , where n12 is refractive index ofedium 1 wth respect to medium 2 .

It can also be easily proved , 

n23 = n21 x n13  

From the laws of refraction it can be proved that when a ray of light pass through a rectangular glass slab the incident ray and emergent ray are parallel. Another familiar example is : the bottom of tank filled with water appears to be raised . It can shown that apparent depth h1 is real depth h divided by refractive index of the medium . Proof : n = sin I /sin r =  tan i/ tanr ( i, r are small )= h2/h1 ( h2 real depth , h1 apparent depth ) 

Total Internal Reflection: 

When light travel from an optically denser medium to rarer medium at the interface light is partly reflected back to the 1st medium .it is called internal reflection . But the refractive angle is greater than incident angle i.e retracted ray bends away from the normal .If we increase the incident angle at a particular value of it refractive angle becomes 90 degree. Any further increase of refractive angle is not possible. This angle of incidence for which refractive angle is 90 degree is called critical angle of the two media .If incident angle is increased greater than critical angle light will get reflected totally from the interface between the two medium .This reflection is Total Internal Reflection.

In the figure above anglevAO3N is critical angle (ic) for the given pair of media . 

So ,Sinic = n21

Hence n12 = 1/Sinic 

Refractive index and critical angle of some media is given below :

Water  =  refractive index 1.33 Critical angle 48.75 degree 

Crown glass = 1.54 , 41.14 

Denser flint glass = 1.62 , 37.31 

Diamond = 2.42 , 24.41

A demonstration for total Internal  Reflection: 

Take a glass beaker with clear water in it . Add a few drops of milk to make it a little turbid .Take a laser pointer and shine it's beam through the turbid water .The path of the last light rays can be seen inside the water .Shine the beam from below the beaker and it strikes the upper layer of water . We can see the beam is divided into two parts at the surface, one is transmitted to the air and the other is reflected back into the water. If we increase the incident angle gradually we find a value of incident angle there is no rays transmitted into the air ,the total rays is reflected into the water . This is total Internal Reflection. 

Total internal reflection in nature and it's technological applications : 

i) 

Prism : prism designed to bend light by 90 degree or 180 degree make use of total internal reflection.Such a prism is used to invert images without changing their shapes .In this case critical angle of the glass making the prism must be less than 45 degree .

ii) Optical fibres : Optical fibres are extensively used to transmit audio and vedio signal for long distance using the total internal reflection. Each fibre consists of two parts one is core and the external part is called cladding .The refractive index of the core material is greater than that of cladding . When a signal in the form of light is directed at one end of the fibre at a suitable angle it undergoes repeated total internal reflections along the length of the fibre and finally comes out of the other end . Since the rays undergoes total internal reflection there is no appreciabke loss of intensity of the light signal . Optical fibres are also used as 'light pipes' to facilitate visual examination of internal organs like stomach and intestines . In decorative lamp optical fibres are used.One end of the fibre is held at the light source and from the other end we get a dot of light .

Refraction at Spherical Surfacesand by  Lenses : 

So far we considered only refraction at plane interface . We shall now consider refraction at Spherical interface seprating between two transparent media . An infinitesimal part of a spherical surface can be considered as plane surface and the law of reflection hold good . The normal at the point of incidence is perpendicular to the tangent plane drawn at the point of incidence. First we consider refraction by a single spherical surface and then follow it by thin lenses .A thin lens is a transparent medium bounded by two surfaces , at least one of which should be spherical .Applying the formula of image formation by a single surface to two surfaces of a lens we will get lens maker formula .

Refraction at Spherical surface : 

In the figure O is a point on the principal axis and I is it's image and R is radius of curvature.The rays are incident from a medium of refractive index n1 to another of refractive index n2 .We take the aparture of the surface is small compared to other distances involved. NM will be taken perpendicular to principal axis .For small angles ,

 tanNOM = MN/OM 

and tan NCM = MN/MC 

tan NIM= MN/MI 

For triangle NOC,  i is exterior angle 

Hence , i = angle NOM + angle NCM 

i = MN/OM + MN/MC 

Similarly , r = angle NCM - angle NIM 

or, r = MN/MC - MN/MI 

By Snell's law 

n1 sini  = n2 sin r 

For small angles , n1 i = n2 r 

n1( MN/OM + MN/MC) = n2(MN/MC - MN/MI) 

Or, n1/OM + n2/MI = (n2 - n1)/MC

Now taking sign convention ,

OM = - u , MI = v , MC = R 

So we have ,

n2/v - n1/u = ( n2 - n1)/R 

u is object distance , v is image distance R is radius of curvature.n1 and n2 are refractive indices of 1 and 2 medium respectively.

Refraction at Convex lens : 

The image formation can be seen in terms of two steps .

The first refracting surface  forms the image I1 of the object O .The image I1 acts as a virtual object for the second surface that forms the image I .Applying the formula for refraction at Spherical surface to the first surface ABC we get , 

n1/OB + n2/BI1 = (n2 -n1)/BC1

A similar procedure applied to the second interface  ADC we get ,

-n2/DI1 + n1/DI = (n2 - n1)/DC2 

For a thin lens BI1 = DI1 and adding the above two equations , 

n1/OB + n1/DI = (n2 -n1)(1/BC1 + 1/DC2) 

If  the object is taken to infinity then OB tends to infinity and DI = f  the above equation gives ,

n1/f = (n2 - n1)( 1/ BC1 + 1/DC2) 

Now BC1 = + R1 and DC2 = -R2 

So the equation becomes 

1/f =( n21 - 1)( 1/R1 - 1/R2) as n21 = n2/n1 

The above equation is known as lens maker's formula .

The formula is equally valid for concave lens also .In concave lens R1 is nagative , R2  positive giving f negative .

Derivation of thin lens formula : 

Considering the refraction at two spherical surfaces , we have the equation : 

n1/OB + n1/DI  = ( n2 - n1)( 1/ BC1 + 1/BC2) 

Or 1/OB + 1 /DI = (n21 - 1)(1/R1 - 1/R2 ) ( OB is object distance = -u, DI is image distance = v and using lens maker formula )

Or , 1/-u + 1/v = 1/f 

Or, 1/v - 1/u  = 1/f 

It is known as lens formula for thin lens .

Image formation by a lens : 

To locate the image of a point of an object kept on th principal axis we have to follow the path of any two rays emerging from the point and undergoes refraction at the lens and then find the point where the refracted rays meet .This meeting point is called the image of the point .

We may consider any two of the following three rays undergoing refraction. 

i) A ray emanating from the point and parallel to the principal axis after refraction passes through the second focus F' 

ii) A ray passing through the optical centre passes undeviated after refraction.

iii) A ray emerging from the object and passing through the 1st focus emerges parallel to the principal axis

 In case of concave lens the rays will not meet after refraction but they seem to come out from a point .

Power of a lens :

The power of a lens is a measure of convergence or divergence of a lens when light falling on it . The power P is the tangent of the angle by which it is converged or diverged when light falling parallel to principal axis falling at a unit distance from optical centre .

tan (delta) = h/f ; if h = 1, then tan(delta)= 1/f 

Delta= 1/f 

Delta = 1/f for small values of delta 

P = 1/f 

The SI unit of power 1D = 1 m^-1 

The power of 1 metre focal length lens is 1 doipotre . It is positive for converging lens and negative for divergence lens .

Combination of thin lenses in contact : 

we consider two lenses A and B of focal length f1 and f2 placed in contact with each other .Let an object is placed at O . The lens A produced an image of I1 . It serves as object to the lens B and final image is formed at I .Let the object distance is u and image distance for I1 is v1 and final image I is formed at a distance v from the lens combination. From the image formed by the first lens A we have , 

1/v1 - 1/u = 1/f1 

For the image formed by 2nd lens B we have , 

1/v -1/v1 =  1/f2 

From the above two relations we get ,

1/v - 1/u = 1/f1 + 1/f2 ,

From the above relation we can say that if the focal length of the combination is f then 

1/f = 1/f1 + 1/f2 

Here two lenses can be regarded as a single lens with focal length f 

If there are more than two lenses the formula can be written as 

1/f = 1/f1 +1/f2 + 1/f3 + ........

So the power of the equivalent lens is P = P1 +P2 +P3 +.........

If the individual magnification is m1 ,m2,m3 etc then total magnification m is given by 

m = m1 m2 m3 .......

Such a combination is used to design lens for cameras, microscope and telescope etc 

Refraction through a prism : 

The picture above shows the refraction of a light rays through a prism . The angle of reflection incidence at the first surface is i and r1 for the second surface the corresponding angles are r2 and e .The angle between incident rays and emergent ray is delta ( ∆) 

In the quadrilateral AQNR , the angles at Q and R are right angles .So the sum of other angles is 180 degree 

Angle A + angle QNR = 180 degree 

From the triangle QNR , r1 + r2 + QNR = 180 degree 

Comparing the above two equations 

A = r1 +r2 

The total deviation delta is the sum of deviations at two surfaces 

∆ = ( i - r1 ) + ( e - r2) 

Thus ∆ = i + e - A 

Thus angle of deviation depends on the angle of incidence i . For any value of delta we have two values i and  e since path of light is reversible. 

At the minimum deviation i = e and hence r1 = r2 .So we have at minimum deviation 

2r = A or r= A/2 

So Dm = 2i - A 

Or i = ( A + Dm)/2 

So the refractive index of the prism 

n21 

= n2/n1 

= sin[(A + Dm)/2]/sin[A/2]

= (A + Dm)/2÷ A/2 ( for angles ,thin prism )

Dm = (n21 - 1) / A 

It means prism do not deviate light much .

Optical Instruments : 

A number of optical devices are designed utilising the property of refraction and reflection. Microscope , telescope and binocular are formed using the above properties of light .

The Microscope : 

A simple microscope is converging lens with small focal length . The lens is held near the object and the eye is positioned close to the lens on the other side .An erect virtual image is formed at a distance so that it can be seen comfortably i.e 25 cm more .If the object is placed at f the image is at infinity.Although if the image is formed at D = 25 cm for comfortable viewing it causes some strain on the eyes . Therefore for relaxed eye comfortable viewing distance is infinity . The linear magnification, 

m = v/u  = v( 1/v - 1/f) = ( 1 - v/f) .

If v= D , for clear vision and using the sign convention, 

m = ( 1 + D/f) , here D is about 25 cm . magnification can also be written as m = h'/h where h' is image size ,and h is object size 

If ,theta is the angle subtanded by object kept at D then 

tan 'theta' = h/D = theta, for small angle . 

This is one less than the magnification when the image is at near point .

In discussion of microscope and telescope we assume image is at infinity.

A simple microscope has a limited maximum magnification (< 9 ) for realistic focal length . For much larger magnification one uses two lenses compounding the effect .This is known as compound microscope.

The lens nearest to the object called objective form real inverted  magnified image .This serves as object for the second lens called eye piece that functions as simple microscope producing enlarge virtual image .

β

magnification produced by objective m zero = h'/h = L/fo .

magnification produced by eyepiece me = 1 + D/fe 

For infinity focusing 

me = D/fe 

The final magnification,

m = mo me =( L/fo) (D/fe)

 Telescope: 

The telescope is used to see distant objects and it provides angular magnification. The angular magnification can be written as the ratio of  angle subtainded by image and the angle that makes by the object at the objective .

So , m = mo .me 

Or , m = tan β/ tan α = h/fe ÷h/fo 

Hence ,m = fo/fe 

Terrestrial telescope has in addition a pair of investing lens to make the final image erect. Refracting telescope can be used as both astronomical and terrestrial observation.

The main considerations with astronomical telescope are its light gathering power and its resolving power .The former is clearly depends on area of objective .With larger diameter of objective fainter objects can be seen .The resolving power is the ability to observe two distinct separated by small angular separation . it also depends on diameter of objective . But it is very difficult and expensive to make very large size lens that are free from also chromatic aberration and distorsion .For these reason modern telescope use concave mirror objective. Such telescope is called reflecting telescope .

One problem of the reflecting telescope is that it focuses light inside the telescope tube . One must have an observer and eye piece there obstructing some light .The solution to the problem is to deflect light bring focused by another convex mirror and the reflecting light passes through a hole in the objective.