Geometrical Optics Questions and Answers

18 If a prism having refractive index 2 has angle of minimum deviation equal to the angle of refraction of the prism then the angle of refraction of the prism is A 30 B 45 C 60 D 90

H Consider the situation in figure The bottom of the pot is a reflecting plane mirror Refractive index of water is a At what distance s from itself will the fish see the image s of the eye b At what distance s from itself will the eye see the image s of the fish Eye H Fish TH 2

A glass hemisphere of refractive index 4 3 and of radius 4 cm is placed on a plane mirror A point object is placed at distance d on axis of this sphere as shown If the final image is at infinity then find the value of d in cm 1 3 3 2 EVER F 4 3 14 cm FASURAT 2 7 4 4

ylindrical vessel of diameter 12 cm contains 800m cm of water A cylindrical glass piece of diameter 8 0 cm and height 80 cm is placed in the vessel If the bottom of the vessel under the glass piece is seen by the paraxial rays see figure 18 E6 locate its image The index of refraction of glass is 1 50 and that of water is 1 33 Water 8 cm 18 cm 12 cm Figure 18 E6

5 Choose the wrong statement A A ray entering a material of larger index of refraction bends toward the normal B A ray entering a material of smaller index of refraction bends away from the normal C A ray oriented along the normal does not bend regardless of the materials D Light rays from any submerged object bend away from the normal when they emerge into the air E When a wave passes from one material into a second material with larger index o refraction the wave speed increases Space for rough work

13 The dotted part of the lens is cut and kept 1 on the x axis as shown in the diagram If parallel paraxial rays are falling on this system then the coordinate of image formed after refraction from both the lenses is 30 1 If x 2 5 then all the distance is in cm Assume lens have no spherical aberration 1 y 2 cm 2 y 6 cm 3 y 4cm 4 y 4 5 cm X y 0 0 X

1 2 A boy is 1 8 m tall and can see his image in a plane mirror fixed on a wall His eyes are 1 6 m from the floor level The minimum length of the mirror to see his full image is 1 0 9 m 2 0 85 m 3 0 8 m 4 can t be determined An object shaped as L is placed between two parallel plane mirrors as shown In the first seven closest images how many laterally inverted images are formed 1 1 4 4 14 2 2 3 3 A plane mirror is placed horizontally on level ground at a distance of 60 m from the foot of a tower Light rays from the top of tower falling just on the edge of the mirror suffers a deviation of 90 The height of the tower is 1 30 m 2 60 m 3 90 m 4 120 m A plane mirror makes an angle of 30 with the horizontal If a vertical ray strikes the mirror find the angle between the mirror and the reflected ray Figure shows the plane top view of a cubical room with the wall CD as a plane mirror each side of the room is 3 metres in length A camera P is placed at the mid point of the wall AB At what distance should the camera be focused A P O B

Q 2 The radius of curvature of a spherical mirror is 20 cm What is its focal length

PE QUESTION 4 0 The refractive indices of the crown glass for blue and red light are 1 51 and 1 49 respectively and those of the flint glass are 1 77 and 1 73 respectively An isosceles prism of angle 6 is made of crown glass A beam of white light is incident at a small angle on this prism The other flint glass isosceles prism is combined with the crown glass prism such that there is no deviation of the incident light Determine the angle of the flint glass prism A prism of refracting angle 30 is coated with a thin film of transparent material of refractive index 2 2 on face AC of the prism A light of wavelength 6600 is incident on face AB such that angle of incidence is 60 Find the angle of emergence

A point object is placed in front of a thick plane mirror as shown in figure Find the location of final image w r t object 1 15 2 cm 3 40 3 cm 10 cm 3 2 5 cm 2 15 cm 4 80 3 cm

Figure show a mirrored equiconvex lens placed at 12 cm below water Find position of object above the surface of water in cm such that its image coincides with itself O 12 cm Hair 1 Hair 4 3 Mg 3 2 R 30cm

In the diagram shown the lens is moving towards the object with a velocity 2 m s and the object is also moving towards the lens with the same speed What is speed of the image with respect to earth when the object is at a distance 2f from the lens f is the focal length V

24 23 vertically A sin 3 5 B sin 4 5 In the figure shown a point object O is placed in air A spherical boundary separates two media AB is principal axis The refractive index above AB is 1 6 and below AB is 2 0 The separation between the images formed due to refraction at spherical surface is B 21 m D 10 m A 12 m C 14 m 2m 1 6 2 0 B 208

A convex lens forms a real image 16 mm long on a screen If the lens is shifted to a new position without disturbing the object or the screen then again a real image of length 81 mm is formed The length of the object must be 1 48 5 mm 3 6 mm 2 36 mm 4 72 mm

A biconvex lens has a radius of curvature of magnitude 20 cm Which one of the following options describe best the image formed of an object of height 2 cm placed 30 cm from the lens 1 5 1 Virtual upright height 1 cm 2 Virtual upright height 0 5 cm 3 Real inverted height 4 cm 4 Real inverted height 1 cm

5 A ray of light travelling in air falls on the surface whose refractive index is 2 If the angle of incidence is 45 find angle of refraction

A prism of refractive index 2 has refracting angle 60 Answer the following questions In order that a ray suffers minimum deviation it should be incident at an angle A 45 B 90 C 30 D none Angle of minimum deviation is A 45 B 90 c Angle of maximum deviation is A 45 C 30 sin 2 sin15 C 30 B sin 2 sin15 D none D none

0 A light ray travelling in glass medium is incident on glass air interface at an angle of incidence 9 The reflected R and transmitted T intensities both as function of 0 are plotted The correct 201 sketch is A B C 100 100 Intensity 0 Intensity 0 T R T R 0 0 90 90 D 100 Intensity 0 100 Intensity T R 0 R 0 0 90 90 2011

25 A ball is dropped from a height of 20 m above the surface of water in a lake The refractive index of water is 4 3 A fish inside the lake in the line of fall of the ball is looking at the ball At an instant when the ball is 12 8 m above the water surface the fish sees the speed of ball as 1 9 m s 2 12 m s 3 16 m s 4 21 33 m s

1 31 is incident on a plane mirror After reflection it travels A ray of light travelling in the direction along the direction 1 31 The angle of incidence is A 30 B 45 C 60 JEE 2013 Advanced 3 60 1 D 75

2015 see stope On a hot summer night the refractive index of air is smallest near the ground and increases with height from the ground When a light beam is directed horizontally the Huygens principle leads us to conclude that as it travels the light beam 1 goes horizontally without any deflection 3 bends upwards 2 bends downwards 4 becomes narrower

Diameter of a plano convex lens is 6 cm and thickness at the centre is 3 mm If the speed of light in the material of the lens is 2 x 108 m s the focal length of the lens is CPMT 1989 JEE Mains 2013 b 20 cm d 10 cm a 15 cm c 30 cm

ICS A convex lens is used to form an image of an object on a screen If the upper half of the lens is blackened so that it becomes opaque Then A Only half of the image will be visible 2011 B the image position shifts towards the lens C the image position shifts away from the lens D the brightness of the image reduces Dob

A light ray I is incident on a plane mirror M The mirror is rotated in the direction as shown in the figure by an arrow at frequency 9 rps The light reflected by the mirror is received on the wall W at a distance 10 m from the axis of rotation When the angle of incidence becomes 37 the speed of the spot a point on the wall is V x 102 m s Find the value of V M 37 10m ito principal optical axis

2 nsider the situation shown in figure 18 E16 The elevator is going up with an acceleration of 2 00 m s and the focal length of the mirror is 120 cm All the surfaces are smooth and the pulley is light The mass pulley system is released from rest with respect to the elevator at t 0 when the distance of B from the mirror is 42 0 cm Find the distance between the image of the block B and the mirror at t 0 200 s Take g 10 m s EA mB M a 2 00 m s 2 Figure 18 E16

image a at 76 A gun of mass M fires a bullet of mass m with a horizontal speed V The gun is fitted with a concave mirror of focal length f facing towards the receding bullet Find the speed of separation of the bullet and the image just after the gun was fired

A point source S is placed midway between two converging mirrors having equal focal length f as shown in figure 18 E3 Find the values of d for which only one image is formed ST

Illustration 40 A compound microscope consists of an objective of focal length 1 0 cm and an eyepiece of focal length 5 cm separated by 12 2 cm At what distance from the objective should an object be placed to focus it properly so that the final image is formed at the least distance of clear vision by Calculate the angular magnification

Illustration 38 If a luminous point is moving at a speed vo towards spherical mirror of focal length f along its axis find the speed of the image

6 A right prism is to be made by selecting a proper material and the angles A and B BSA as shown in figure 18 W5a It is desired that a ray of light incident normally on AB emerges parallel to the incident direction after two total internal reflections a What should be the minimum refractive index u for this to be possible b For u 5 3 is it possible to achieve this with the angle A equal to 60 degrees

ration 36 A thin plano convex lens of focal length f is split into two halves One of the halves is shifted along the principal axis as shown The separation between an object placed on the axis and its image is 1 8 m The magnification of the image formed by one of the half lenses is 2 Find the focal length of the combination and the separation between the two halves Object Image

A U shaped wire is placed before a concave mirror having radius of curvature 20 cm as shown in figure 18 E1 Find the total length of the image 10 cm 10 cm 30 cm Figure 18 E1

d n 2 4 Air has refractive index 1 0003 The thickness of air column which will have one more wavelength of yellow light 6000 than in the same thickness of vacuum is a 2mm b 2 cm c 2m d 2km d 2n

A convex lenses of focal length 40 cm is held coaxially 12 cm above a concave mirror of focal length 18 cm An object held x cm above the lens gives rise to an image coincident with it The x is equal to O 2720 104 12 cm b 15 cm x cm 12 cm P 146 c 18 cm d 30 cm

9 a An electromagnetic radiation of wavelength ranging between 400 nm and 1150 nm for which the plate is penetrable incident perpendicularly on the plate from above is reflected from both the air surfaces and interferes In this range only two wavelength give maximum reinforcements one of them is 400 nm refractive index of air 1 and the coefficient of linear of cube 8 x 10 C The thermal expansion distance of bottom of cube from plate does not change during warming up Choose the correct option s cube murm A The change in temperature of cube so that it would touch the plate is 6 2 C B The change in temperature of cube so that it would touch the plate is 3 1 C C The second wavelength which gives maximum reinforcement is 2000 3 4000 D The second wavelength which gives maximum reinforcement is 3 nm nm 400 11 50 Plate h 2 cm

20 Suppose that a ray of light leaves the point 3 4 reflect off the Y axis towards the X axis reflects off the X axis and finally arrives at the point 8 2 The value of x is a 4 0 y O 13 b 4 3 4 x 0 8 2 2 c 4 d 5 3 3 X

k 17 A submarine is 300 m horizontally out from the shore and 100 m beneath the surface of the water A laser beam is sent from the submarine so that it strikes the surface of the water at a point 200 m from the shore If the outgoing beam from the surface of the water just strikes the top of building standing vertically at shore then the height of the building is uw 4 3 a 300m b 140m c 240m d 170 7 m

of convex lens of focal length 40 cm in contact with a concave lens of focal length 25 cm The power of this lens combination in diopters is 1997 2M a 1 5 b 1 5 c 6 67 2 6 67

A plane mirror reflects a pencil of light to form a real ima Then the pencil of light incident on the mirror is MP PMT 1997 DCE 2001 03 KCET Engg Med 200 a Parallel b c Divergent d Convergent None of the above

A ray of light strikes a glass plate at an angle of 60 If the reflected and refracted rays are perpendicular to each other the refractive index of glass is 1 2 1 2 3 3 2 2 3 V2 4 3

6 Speed of light in water is 2 5 x 10 m s and in glass is 2 x 10 m s which has higher refractive index 15

Two similar thin equi convex lenses of focal length feach are kept coaxially in contact with each other such that the focal length of the combination is F When the space between the two lenses is filled with glycerin which has the same refractive index p 1 5 as that of glass then the equivalent focal length is F2 The ratio F F will be 2 1 1 2 2 3 3 4 1 2 3 4

Two plane mirrors are placed as shown in the figure and a point object O is placed at the origin mis JN me Sonal ay How many images will be formed Find the position s of image s Will the incident ray passing through a point P 1 1 25 take part in image formation 0 0 0 1 1 25 P object 2 4 2 3 2 2 2 0

The image of an object formed by a plano convex lens at a distance of 8 m behind the lens is real and is one third the size 2 of the object The wavelength of light inside the lens is times 3 the wavelength in free space The radius of the curved surface of the lens is JEE 2013 a 1 m e 3 m b 2 m d 6 m

6 A water proof laser pointer of length 10 cm placed in a water tank rotates about a horizontal axis passing through its center of mass in a vertical plane as shown in the figure The time period of rotation is 60 s Assuming the water to be still and no reflections from the surface of the tank the duration for which the light beam escapes the tank in one time period is close to Refractive index of water 1 33 40 cm a 8 13 s c 16 27 s 30 cm Laser 10 cm 30 cm b 14 05 s d 23 86 s

the blanks with the correct words The band of light that is produced when white light is split is called dispersion spectrum

10 n A glass prism is immersed in a hypothetical liquid The curves showing the refractive index n as function of wavelength for glass liquid When a ray of white light is incident on prism parallel to the base liquid glass Base Ayellow A yellow ray travels without deviation B blue ray is deviated towards vertex C red ray is deviated towards base D These is no dispersion

The distance between an object and a divergent lens is m times the focal length of the lens The linear magnificatio produced by the lens is WB JEE 2009 a m e m 1 b 1 m 1 d m 1

An object placed at a distance of 9cm from first principal focus of convex lens produces a real image at a distance of 25cm from its second principal focus Then focal length of lens is 15 1 1 9 cm 2 25 cm men 3 15 cm 4 17 cm

Example 21 Find the ratio of the intensity at the centre of a bright fringe to the intensity at the point one quarter of the distance between two Sigmars fringes from the centre given