Geometrical Optics Questions and Answers

A cubical vessel with non transparent walls is so located that the eye E of an observer can not see its bottom but can see all of the wall CD The height upto which water should be filled in the vessel for the observer to see an object O as 4 shown will be OC 10 cm of water 3 1 25 cm hipe A ID 2 26 7 cm

3 A thin biconvex lens of refractive index is placed on a horizontal plane mirror as 2 shown in the figure The space between lens and the mirror is then filled with water of refractive index 46 17 4 It is found that when a point object is placed 15 cm above the lens on the principal axis the object coincides with its own image 1 5 R 1 3 YOLUTU VI TONTO What is value of R from above information A R 10 cm C R 5 cm 2 B R 15 cm D R 20 cm

1 A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it the final image would be formed at a distance of 2 3 4 60 cm 40 cm cm 60 20 cm from the plane mirror it would be a virtual image 20 cm from the lens it would be a real image 30 cm from the lens it would be a real image 30 cm from the plane mirror it would be a virtual image

Image in convex mirror of the image of rod PQ in the plane mirror is radius of curvature of mirror is 60 cm 5 cm PH 15 cm 5 cm 1 Virtual erect and 6 cm long 2 Real inverted and 3 cm long 3 Virtual erect and 3 cm long 4 Real inverted and 6 cm long

What is the maximum angle of incidence in the figure for which the ray would satisfy the ondition for total internal reflection at the boundary of media of refractive indices n and n here n n 0 0 air 0 sin n n 0 sin n n 0 sin 1 0 sin n n 2 n n

Show with detailed solutions and formula derivations if t here is any 15 m 53 f 10cm 30cm Find velocity of image

Q46 A transparent slab of thickness d has a refractive index n z that increases with z Here z is the vertical distance inside the slab measured from the top The slab is placed between two media with uniform refrac tive indices ni and n2 n as shown in the figure A ray of light is incident with angle 0 from medium 1 and emerges in the medium 2 with refraction angle of with a lateral displacement 1 Which of the following statement s is are true 2016 n1 const I n z 2 n2 const 0 KI n sin 0 n2 sin Of B n sin 0 n n sin f is independent of n I 1 TKBI2 d

A mirror always forms virtual image of the magnification unity The focal length of the mirror is Less than 1 m but not zero Greater than 1 m but not infinity 1m

Q45 A plano convex lens is made of material of refrac tive index n When a small object is placed 30 cm away in front of the curved surface of the lens an image of double the size of the object is produced Due to reflec tion from the convex surface of the lens another faint image is observed at a distance of 10 cm away from the lens Which of the following statement s is are true 2016 The refractive index of the lens is 2 5 B The radius of curvature of the convex surface is 45 cm C The faint image is erect and real The focal length of the lens is 20 cm

A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since 1 2 3 4 a large aperture contributes to the quality and visibility of the images a large area of the objective ensures better light gathering power a large aperture provides a better resolution all of the above

3 A convex lens A of focal length 20 cm and a concave lens B of focal length 5 cm are kept along the same axis with a distance d between them If a parallel beam of light falling on A leaves B as a parallel beam then the distance d in cm will be 1 2 3 4 50 30 15

9 NO 20 View in English A thin equiconvex lons has focal length 10 cm and refractive index 15 One of its faces is now silvered and for an object placed at a distance u in front of it the image coincides with the object The value of u is 1 2 3 4 Correct Answer 2 Status unattempted 10 cm 5 cm 20 cm 15 cm

An object is placed at a distance f 2 from a convex lens The image will be 1 At one of the foci virtual and double in size 2 3 At 2f virtual and erect 4 At f real and inverted At 3 2 f real inverted

An equiconvex air lens R R 10 cm is made in an glass medium having refractive index 3 2 changes magnitude A 3 2 C 1 8 Find the refractive index of the material to be filled in so that the power of the lens without change in its B 2 D 1 2 fi

1 Two plane mirrors are inclined at 70 A ray incident on one mirror at angle q after reflection falls on the second mirror and is reflected from there parallel to the first mirror qis a 50 b 45 c 30 d 55

A cubical transparent slab is used as a paper weight What should be the minimum refractive index the material of the slab so that letters below it are not visible from any of its vertical faces A 2 C s B 3 D 5 3

C 12 22 D 9 Q 28 A four times magnified image was formed by a spherical mirror for the two object distances eithe 9 cm or 16 cm Focal length of the mirror is A 12 cm C 21 cm B 12 cm D 21 cm 30 ww 1202

A ray of light is travelling from glas Refractive index of glass is 3 2 If the angle of incidence is 57 then the deviation of the ray is cosec 42 1 5 1 57 3 57 sin 1 sin 57 3 2 Ve 66 sin 1 sin 57 3 2 57

A person is unable to read the newspaper but he can read it by shifting it some distance further H is suffering from 1 Myopia 2 Hypermetropia 3 Cataract 4 Colour blindness

8 A convex lens and a concave lens are kept in contact with common principal axes If f and f represents the focal length of the convex lens and concave lens respectively then If f 2 cm and f 5 cm then the equivalent focal length of the combination is 1 3 cm 2 7 cm 3 10 3 cm 4 10 3 cm

A plano convex lens behave as a concave mirror of focal length 30 cm when its plane surface is silvered and as a concave mirror of focal length 10 cm when its curved surface is silvered The radius of curvature of curved surface in cm is x 10 cm A 2 3

An object lies in front of a convex surface as shown in the figure First principal focus f 20 cm and second principal focus f 40 cm The position of f2 image if x 30 cm is 30 k cm from the pole Then find the value of K O X P H

A convex lens of focal length 10 cm is cut along the line AB as shown in the figure a The parts of the lens are combined as shown in the figures i ii iii iv The focal lengths in these cases are f 12 f3 14 respectively M D M D 1 compare these focal lengths 1 18 A B D f f f f f f f f f f f f None of these 111 iv

For the given incident ray as shown in figure the condition of total internal reflection of this ray the required refractive index of prism will be a c 3 1 2 E mic b d 1 2 INO 45 incident ray 200

The sun subtends an angle of 0 5 when seen from the Earth If the image of the sun is formed with a convex lens of focal length 50 cm what will be the approximate diameter of the image of the sun A 8 mm B 4 mm C 1 mm

5 Find the maximum value of r R so that the beam of light incident normally at the face A of a U shaped glass tube emerges through B as shown in he figure The refractive index of glass is 1 5 R

ray of light is incident on the first mirror at an angle of incidence e 2 Then the reflected ray from the second mirror will make an angle of reflection 1 0 2 0 2 3 0 3 10 200 quafda far fay queda sin ti 1 0 2 8 2 3 0 3 foran a faca d

When upper half of the lens is covered by an opaque screen 1 Half the image will disappear 2 Complete image will be formed of same intensity 3 Half image will be formed of same intensity 4 Complete image will be formed of decreased intensity 1 2 f ff 3 4 f treate and en fee

2 A ray of light that strikes a plane mirror PQ at an angle of incidence of 30 is reflected from the plane mirror and then strikes a second plane mirror QR placed at right angles to the first mirror The angle of reflection at the second mirror is a 30 b 45 c 60 d 90

A plane mirror OA of length 2 m is kept along the line y x as shown in the figure An insect having velocity of 41 cm s is moving along the x axis from far away The time span for which the insect can see its image will be

23 There are two plane mirror with reflecting surfaces facing each other Both the mirrors are moving with the speed v away from each other A point object is placed between the mirrors The velocity of the image formed due to nth reflection will be 1 nv 2 2nv 3 3nv 4 4nv

127 A glass prism u 1 5 is dipped in water u 4 3 as shown in figure A light ray is incident normally on the surface AB It reaches the surface BC after totally reflected if B 1 sin0 8 9 2 2 3 sine 8 9 3 sine 2 3 4 It is not possible 0 A

20 Light traveling through three transparent substances follows the path shown in figure Arrange the indices of refraction in order from smallest to largest Note that total internal reflection does occur on the bottom surface of medium 2 1 1 1 11 2 n 1 n 11 2 1 1 1 4 n 1 1

1 10 cm 3 20 cm A light pipe is made of glass fibre of refractive index 1 57 The outer covering of the pipe is made of a material of refractive index 1 36 The range of angles of incident 2 15 cm 4 25 cm rays with the axis of the pipe for which total internal reflection inside the pipe take place is nearly NCERT Pg 345 1 0 i 38 3 0 i 60 2 0 i 90 4 0 i 53

A plano convex lens having a radius of curvature of r 4 00 m is placed on a concave glass surface whose radius of curvature is R 12 0 m as shown in Figure P37 65 Determine the radius of the 100th bright ring assuming 500 nm light is incident normal to the flat surface of the lens 1 R

Consider the situation shown in the figure Two slits S and S are placed symmetrically about the line OP which is perpendicular to screen The space between screen and slits is filled with a liquid of refractive index A plate of thickness t and refractive index is placed in front of one of the slit A source S is placed above OP at a distance d Choose the correct alternatives 1 Given that D 1m d 2 mm 1 6 10 m 1 2 1 8 Screen air air B D 2D Hy P Position of central maxima from point P is NG mm Thickness of glass slab so that central maxima

A plano convex lens has a thickness of 4 cm when placed on a horizontal table with curved surface in contact with it the apparent depth of the bottom most point of the lens is found to be 3 cm If the lens is inverted such that the plane face is in contact with the table the apparent depth of the center of plane face is found to be 25 cm The focal length of the len as measured from center of spherical surface can be 8

REFRACTION AT LENS A boy is trying to start a fire by focusing sunli a piece of paper using an equiconvex lens of length 10 cm The diameter of the sun is 1 39 x and its mean distance from the earth is 1 5 x 10 What is the diameter of the sun s image or a 6 5 x 10 5 m b 12 4 x 10 c 9 2 x 10 m d 6 5 x 107

A liquid of Refractive index 1 6 is contained in the cavity thin of a glass specimen of refractive index 1 5 as shown in the figure If each of the curved surface has radius of curvature of 0 20 m then the arrangemen behaves as a Glass Liquid 1 Converging lens of focal length 0 25 m 2 Diverging lens of focal length 0 23m 3 Diverging lens of focal length 0 17m

2 A biconvex lens of focal length 10 cm is to be made on glass material If refractive index of the material is 1 5 what must be the radius of curvature of surface of the lens a 0 1 m c 0 20 m b 0 15 m d 0 30 m

38 The angle of a prism is A and if the angle of 3 minimum deviation is 180 2A then the refractive index of the material of the prism is NCERT XII II 331 1 sin A 2 2 cos A 2 3 tan A 2 4 cot A 2 augh air with a

12 I For the given incident ray as shown in figure the condition of total internal reflection of the ray will be satisfied if the refractive index of block will be AIPMT 2002 3 1 2 1 2 45 Incident ray 3 2 4 76 mure Let f f f be the

1112 m m 3 m m 2 For which of the following colour the magnifying power of a microscope 1 White colour 2 Red colour 3 Violet colour The length 4 m x m X will be maximum 4 Yellow colour

A compound microscope consists of an objective lens of focal length 0 8 cm and an eyepiece of focal length 3 2 cm which are separated by a certain distance An object is placed at a distance of 1 cm from the objective If the final image is formed at infinity the distance between the lenses is A 7 2 cm B 4 8 cm C 4 cm D 3 2 cm A FD

In Fig ABC is the cross section of a right angled prism and ACDE is the cross section of a glass slab The value of 0 so that incident normally on the face AB does not cross the face AC is given sin 1 3 5 37 B n 3 2 0 37 0 37 0 53 9 U C D Correct

A ray of light PQ is incident at angle i on a prism face See figure After 2 refractions it leaves the prism at a grazing angle B If u is the refractive index and B is the refractive index and B is the refracting angle of the prism the refracting index u is 1 sin i cos B sin R Correct

3 Deviation and dispersion 4 None of the above The ratio of angle of minimum deviation of a prism in air and when dipped in water will be 3 2 and If prism angle is very small 1 1 8 2 1 2 3 3 4 4 1 4 the flint and crown glass prisms are A and A They are to be used for dispersion

10 Problem 9 A camera lens used for taking close up photographs has a focal length of 27 5 mm The farthest it can be placed from the film is 31 5 mm 50 Part a What is the closest object that can be photographed in cm

40 An object and its real image are located at distances cm and 40 cm respectively from the two principal foci of convex lens The lateral magnification of the image is 2 1 3 1 1 3 3 1 8 4 1 8

f and f both become negative ght is incident from a medium into air at two possible gles of incidence A 20 and B 40 In the medium light avels 3 0 cm in 0 2 ns The ray will suffer total internal reflection in both cases A and B suffer total internal reflection in case B only have partial reflection and partial transmission in case B O have 100 transmission in case A