Geometrical Optics Questions and Answers

20 A luminous point object is moving along the principal axis of a concave mirror of focal length 12 cm towards it When its distance from mirror is 20 cm its velocity is 4 cm s The velocity of the image in cm s at that instant is a 6 cm s towards the mirror b 6 cm s away from the mirror c 9 cm s away from the mirror d 9 cm s towards the mirror c 1 0 24 How heig the t a 8 25 Mor

1 M 30 A ray of light strikes a transparent rectangular slab of refractive index 2 at an angle of incidence of 45 The angle between the reflected and refracted ray is a 75 b 90 c 105 d 120 A transparent cube of 15 cm edge contains a small air

d 43 2 Refractive index of a medium is The incidence angle is twice that of refracting angle The angle of incidence is a cos c 2 cos 2 b sin 2 d sin u 2 16 In vacuum to travel dicto C 51 TH are a C 52 De is pr a 53 Ar

52 Deviation of 50 is observed from a prism whose angle is small and whose refractive index is 1 5 The angle of prism is a 7 5 d 3 3 b 10 c 5 53 Angle of prism is A and its one surfor 2 The A is m mag

46 In vacuum to travel distance d light takes time t and in medium to travel 5d it takes time T The critical angle of the medium is 5T 0 a sin c sin 5t T b sin d sin 5t T 72 8 5t 37

int object O is placed in front of a glass rod having spherical end of curvature is 30 cm The image would be formed at 9 AIR 15cm a 30 cm left b Infinity c 1 cm to the right d 18 cm to the left GLASS 30cm

A A beam of light of intensity I is normally incident on a plate of area A If plate absorbs fraction of incident light and reflects rest of it back then the force exerted by the incident light on the plate is given by c speed of light 3 2n 1 4 2 1 A steam of water density cross sectional area A and speed u strikes a wall that is

d 18 85 A telescope of objective lens diameter 2m uses light of wavelength 5000A for viewing stars The minimum angular separation between two stars whose image is just resolved by their telescope is a 4 x 10 rad b 0 25 x 10 6 rad c 0 31 x 10 rad d 5 x 10 rad 5 The focal lengths of the obi 90

3 with principal axis then n is O k 450 20 cm f 10 cm The distance between an object and the screen is 100cm A lens produces an image on the scre when the lens is placed at either of the positions 40 cm apart The power of the lens is nearly diopters The given lens is broken into four parts and rearranged as shown If the initial focal length is f then after rearrangement the equivalent focal length is Then Y is

a 5cm b 5cm c 7 5cm d 7 5cm 3 A short linear object of length b lies along the axis of a concave mirror of focal length fat a distance u from the pole of the mirror what is the size of image 2 b a C 15 b f f 16 d u f f b

72 In order to obtain a real image of magnification 2 using a converging lens of focal length 20 cm where should an object be placed a 50 cm c 50 cm b 30 cm d 30 cm 73 The radius of the convex surface of plano convex lens is 20 cm and the refractive index of the material of the lens ah of the lens is

Two plane mirrors A and B are placed such that they make certain angle between them A ray of light is incident on the mirror A The reflected ray from B travels perpendicular to the ray incident at A What is the angle between the two plane mirrors O O O O 60 30 45 70

Two plane mirror A and B are placed parallel to each other and are separated by a distance of 100 cm The distance of the first two image formed in the mirror A from and the object when object is placed 10 cm from mirror B are respectively O O O 180 cm 290 cm 180 cm 190 cm 180 cm 200 cm 180 cm 390 cm

74 The focal length of convex lens for red and blue light are 100 cm and 96 8 cm respectively The dispersive power of material of lens is a 0 325 c 0 98 b 0 0325 d 0 968

89 The maximum magnification that can be obtained with a convex lens of focal length 2 5 cm is the least distance of distinct vision is 25 cm a 10 b 0 1 c 62 5 d 11 90 A compound microscope has an eye piece of focal length

Two liquids A and B are poured in a glass tumbler as shown in the figure If the refractive indices of A and B are 7 3 and 5 3 respectively then the base of the container appears to be at a depth of cm from the free surface of B 35 cm 35 cm O O O O 36 34 35 66 B A

The lens he is using is Concave lens of focal length 0 5 m Convex lens of focal length 2 0 m Concave lens of focal length 2 0 m Convex lens of focal length 0 5 m using a lens having power of 2 D

25 The effective focal length of the lens combination shown in th figure is 60 cm the radii of curvature of the curved surfaces of the plano convex lenses are 12 cm each and refractive index of the material of the lens is 1 5 What would be the refractive index of the liquid Liquid 1 33 h 1 42 c 1 53 d 1 6

ne n 31 Consider the metal coin in figure The right half is polished while left half is unpolished Unpolished Flashlight beam Beye Polished In a dark room this coin is placed face up on the floor and illuminated with a thin beamed flashlight as shown in figure A and B look at the coin from the position as indicated in figure A A eye B hole height h Floor figure The its radius filled with 2h he car rod The the liquid a 5 2 c 3 3 A ray c the left cube of shown incide Coin According to A which half of the coin if either is brighter a The polished half b The unpolished half c Both halves look equally bright page surrou What incid inter

28 A beam is incident on a tube containing two convex lenses of focal length 15 cm and 20 cm as shown If the diameter of incident beam is 10 cm find the diameter of final beam a C 40 3 50 3 cm cm A lens is b d 20 3 25 3 cm cm

c 5 sec d Remains some 45 For the ray diagram shown in the adjoining figure the false statement is Normal 1 P A Normal a 8 i i r 1 b A 1 1 c sin i sin r sin i sin r

3 A prism of a certain angle deviates the red and blue rays by 8 and 12 respectively Another prism of the same angle deviates the red and blue rays by 10 and 14 respectively The prisms are small angled and made of different materials The dispersive powers of the materials of the prisms are in the ratio a 5 6 b 9 11 c 6 5 d 11 9

sin i cos sin 90 i je tan u tan 3 60 sin r tan 4 pla ple 14 One face of a rectangular glass plate of 8 cm thickness is silvered An object held 10 cm in front of the unsilvered face forms an image 12 cm behind the silvered face What is the refractive index of the glass Apparent position of the silvered face is shifted towardin w

From the above discussion it follows that the total time taken from a point on the object to the corresponding point on the image is the same measured along any ray For example when a convex lens focusses light to form a real image although the ray going through the centre traverses a shorter path but because of the slower speed in glass the time taken ens is the same as for rays travelling near the edge of the lens

con Osi 13 In the following ray diagram tions of the object O image I two lenses and a plane mirror The focal length of one of the lenses is also given Calculate the focal length of the other lens Ans 20 cm 0 05 f 20 cm 16 cm 35 cm

Two vertical plane mirrors facing each other 8 m apart A candle is set 2m from one of the mirrors An observer in the middle of the two mirrors looks into the other and sees two distinct images of the candle How far those images from the observer B 8 m 10 m A 10 m 14 m C 6 m 12 m D 7 m 14m

A parallel beam of rays of width 20 cm passing through a glass slab makes an angle 60 with its plane surface If the beam emerges into air from this surface then calculate the width of the emergent beam Refractive index of glass 1 8

3 Young s double slit experiment is performed with light of wavelength 5000 A If a glass plate of thickness 1 um and refractive index 1 5 is kept in front of one of the slits then number of fringes that passes through the field of view is 1 1 d 2 2 3 3 4 4

Two plane mirrors AB and AC are inclined at an angle 0 20 A ray of light starting from point P is incident at point Q on the mirror AB then at R on mirror AC and again on S on AB finally the ray ST goes parallel to mirror AC The angle which the ray makes with the normal at point Q on mirror AB is A 20 B 30 C 40 D 60 P R

A ray of light falls on a plane mirror When the mirror is turned about an axis at right angle to the plane of the mirror through 300 the angle between the incident ray and original reflected ray is 750 The angle between the incident ray and new reflected ray is A 45 B 65 C 75 D 60

Complete the following ray diagrams after taking reflection from the second mirror with the angle of incidence and angle of reflection mentioned for each reflection of light Fin the net angle of deviation i 60 A i 100 240 CW B i 200 225 CW C i 100 225 CW D i 100 225 CW 040 ii ii 450 450 180 CW ii 300 300 180 CW ii 450 450 180 CW ii 600 600 180 CW 90 45 iii 700 700 160 ACW iii 700 700 140 ACW iii 600 60 140 ACW iii 700 70 140 ACW iii 100

When a ray is refracted from one medium to another the wavelength changes from 6000 to 4000 The critical angle for the interface will be Question Type Single Correct Type 1 COS 2 sin 3 sin 2 3 213 1 2

9 In the Young s double slit experiment apparatus shown in figure the ratio of maximum to minimum intensity on the screen is 9 The wavelength of light used is then the value of y is AD d a 1 1 1 1 b d 2 d 2 KD AD 2d Ty c Screen D XD 3d d D 4d

A clear transparent glass sphere 1 5 of radius R is immersed in a liquid of refractive index 1 25 A parallel beam of light incident on it will converge to a point The distance of this point from the centre will be 1 3R 2 3R 3 R 4 R

An electromagnetic wave of frequency v 3 0 MHz passes from vacuum into a dielectric medium with permittivity 4 0 Then a wavelength is doubled and frequency unchanged b wavelength is doubled and frequency becomes half c wavelength is halved and frequency remain unchanged d wavelength and frequency both remain unchanged

An achromatic convergent doublet of two lenses in contact has a power of 2D The convex lens has power 5D What is the ratio of the dispersive powers of the convergent and divergent lenses Question Type Single Correct Type 1 2 5 2 3 5 3 5 2

Two thin similar convex glass pieces are joined together front to front with its rear portion silvered such that a sharp image is formed 20 cm from the mirror When the air between the glass pieces is replaced by water w 4 3 then the image formed from the mirror is at a distance of A 8 cm C 6 cm B 10 cm D 12 cm

As show in figure a convergent lens is placed inside a cell filled with liquid The lens has focal length 20 cm when in air and its material has refractive index 1 50 If the liquid has refractive index 1 60 the focal length of the system is 0 Question Type Single Correct Type 1 2 3 80 cm 80 cm 24 cm

In a thin prism of glass refractive index 1 5 which of the following relations between the angle of minimum deviations Sm and angle of prism r will be correct a 8m r c 8m 2r b 8m 1 5 r d 8m r 2

2 10 Two planoconvex lenses each of focal length 10 cm refractive index 3 2 are placed as shown In the space left water R I 4 3 is filled The whole arrangement is in air The optical power of the system is in diopters A 6 67 B 6 67 C 33 3 D 20

6 An objects is placed 21 cm in front of a concave mirror of radius of curvature 10 cm A glass slab of thickness 3 cm and u 1 5 is then placed close to the mirror in the space between the object and the mirror The position of final image formed is BHU a 3 94 cm c 4 93 cm b 4 3 cm d 3 94 cm

Two point objects 0 and 0 are placed on the principal axis of a concave mirror of radius of curvature 10cm at distance 3cm and 7Cm respectively from the pole If at t 0 the objects start moving towards each other with 1cm s velocity each then at t 0 their images will 1 Move towards each other with relative speed 10 cm s 2 Move away from each other with relative speed 12 5 cm s 3 Move in same direction with equal speed of 5 cm s each 4 Move away from each other with relative speed 10 cm s

A small telescope has a objective lens of focal length 150 cm and an eyepiece of focal length 5 cm If this telescope is used to view a 100 m high tower 3 km away find the height of the final image when it is formed 25 cm away from the eyepiece Delhi 2012 Ans 36 30 cm

Two large plane mirrors M and M are kept at an angle of 120 as shown in figure The co ordinate of intersection of plane mirror is 0 2 meter A man moves along x axis Find the length in meter on x axis for which can see both the images of point A formed by mirrors simultaneously take 3 1 73 and height of man is negligible M man 60 60 A 0 0 M X

3 A ray of light travelling in air is incident on a face of a rectangular slab and comes out from the opposite face The angle between the incident ray and the normal to the surface is 30 What is the angle between the ray coming out of the slab and the normal to the face from which it comes out

A large convex spherical mirror in an amusement park is facing a plane mirror 10 m away A body of height 1 m standing midway between the two sees himself twice as tall as in plane mirror as in spherical one In other words the angles subtended at the observer by the image in plane mirror is twice the angle subtended by the image in the spherical mirror The focal length of the convex mirror is

SolveLancer Test Which of the following is Incorrect i Myopia is corrected by using convex lens ii Presbyopia is corrected by using cylindrical lens iii Hypermetropia is corrected using concave lens iv During rainbow formation total internal reflection does not take place in water droplets SolveLance Test a i ii iv b ii iii c i ii iii iv d i iii

A small candle is kept at a distance of 1 00 m from a screen A lens of focal length 10 0 cm is placed between the candle and the screen There are two positions of the lens that will result in a sharp image of the candle on the screen The distance in m between these two positions is p The value of p is

An object is gradually moving away from the focal point of a concave mirror along the axis of the mirror The graphical representation of the magnitude of linear magnification m versus distance of the object from the mirror x is correctly given by Graphs are drawn schematically and are not to scale A C m m 1 f 2f X f 2f B D 1 1 2f f 2f I

36 A ray enters a medium of origin such that the refractive index varies with y co ordinate as P P constants a a y 3 60 a YA where and a are positive Find the y co ordinate of the point after which the ray becomes parallel to x axis 1 a 2 2a 4 X 1 a 2