Geometrical Optics Questions and Answers

1 A mark M placed on the surface of a glass sphere is viewed through glass from diametrically opposite end If diameter of sphere is 10cm and refractive index of glass 1 5 find position of image from centre of sphere 26 Mope 1 15cm o pops er to 3 10cm Be to 19 ens A 2 20cm of leupe insign 4 25cm 100 north

In a concave mirror an object is placed at a distance d from the focus and the image is formed at a distance d from the focus Then the focal length of the mirror is a djdz b d d c d d d d d 2 AIIMS

A ray of light travelling in glass 3 2 is incident on a horizontal glass air surface at the critical angle 8c If a thin layer of water 4 3 is now poured on the glass air surface the ray of light emerge into air at the water air surface at an angle of k radians from the normal at that point find the value of k C A Water O R 0c R u 3 2 D B

A real object is placed 1 cm above the optical axis of a convex lens of focal length 40cm The object distance is 60cm If the object now starts moving perpendicularly away from the optical axis with a speed 10 cm s the speed of the image is

velocity plane mo of 21 31 6k A mirror whose reflecting surface is parallel to y z plane is moving with a velocity of i k What is the velocity of image as seen by a stationary observer

The top of a swimming pool is at ground level If the pool is 2 90 m deep how far below ground level does the bottom of the pool appear to be locate for the following conditions The index of refraction of water is 1 333 a The pool is completely filled with water Im below ground level b The pool is filled halfway with water m below ground level

A fish in an aquarium 30 cm deep in water can see a light bulb kept 50 cm above the surface of water The fish can also see the image of this bulb in the reflecting bottom surface of the aquarium Total depth of water is 60 cm Then the apparent distance between the two images seen by the fish is w 4 3 A 140 cm C 280 3 cm B D 760 3 380 3 cm cm

A thin lens made of glass of refractive index 1 5 has a front surface 11 D power and back surface 6 D If this lens is submerged in a liquid of refractive index 1 6 the resulting power of the lens is Question Type Single Correct Type 1 0 5 D 2 0 5 D 30 625 D

A slab of glass of thickness 6 cm and refractive index 1 5 is placed in front of a concave mirror as shown in the figure If the radius of curvature of the mirror is 40 cm and the reflected image coincides with the object then the distance of the object from the mirror is A 30 cm C 42 cm O 6 cm 1 5 B 22 cm D 38 cm

23 An object far away moves on the axis of a concave mirror towards it with constant speed upto its focus Its image moves 1 Towards the mirror with constant speed 2 Away from the mirror with constant speed 3 Away from the mirror with constant acceleration 4 Away from the mirror with variable acceleration

3 80 cm 5 cm 4 10 cm 1 cm For a normal eye the distance between the retina and the cornea eye lens is 2 5 cm If least converging power of eye lens is 30D then find converging power of cornea of eye 1 20 D 2 30 D 3 10 D 4 5 D If the focal length of objective lens is decreased then

A ray of light is incident on a prism as shown in the figure The total deviation suffered by the ray is X 2 Then find x BAC 1 and CAD 2 refractive indices are shown in figure A 1 2 n 1 5 n 2

An object O is placed between two parallel mirrors M and M as shown in the figure Find distance between the 2nd image formed by M and 4th image formed by M The first reflection occurs at M M O 20 cm M2 30 cm

n the given circuit if the value of Ra 2 2k ohm Rb 3 9 K ohm and C is 0 1 micro farad then find the positive and negative pulse width with free running frequency RA wwww C RB 3 9 k 2 2 k HH 0 1 F 7 6 Vcc 5 V 80 2 555 1 C 4 578 5 0 01 F 3 Output

7 A ray of light enters a spherical drop of a liquid of refractive index This ray after getting reflected from back surface comes out as shown Given sin41 A Ray suffers total internal reflection at back surface B Total internal reflection at back surface is not possible for any value of 4 C Total deviation suffered by ray Refraction Reflection Refraction is minimum when 60 D When angle of incidence is chosen such that total deviation is minimum then value of total deviation is 136 Air Air

A point object is kept at point P 0 y as shown in the figure Find 3 the value of y so that its image is also formed at point P H 2 Radius of curvature of concave mirror is 130 cm and H 3 radius of curvature of curved part of glass is 30 cm A 21 cm B 30 cm C 39 cm D 40 cm glass Water P 0 y B 0 0 9 cm 42 cm

Question 18 Two glass slabs 1 and 2 of same refractive index are placed in air as shown A point object is placed on the left side of the slab 1 There are two observers A and B observing the object The observer A sees the object 2 cm closer from the actual position of the object while the observer B sees it 3 cm closer from the actual position of the object The ratio of the thicknesses of the slabs 1 and 2 is 2 object 1 B

A spherical mirror forms an erect image three times the linear size of a real object If the distance between the object and the image is 80 cm the focal length of the mirror is 6n cm Find n report nearest integer

1 A thin glass u 1 5 lens has optical power of 10D in air Its optical power in a liquid medium with refractive index 1 6 will be 1 1D 2 2D 3 1 25 D 4 2 5 D ou

8 Figure shows a thin converging lens for which the focal length is 5 cm The lens is in front of a concave spherical mirror of radius R 30 cm If the lens and mirror are 20 cm apart and an object is placed 15 cm to the left of the lens determine the approximate distance of the final image from the lens in cm 1 5 3 cm 2 4 6 cm 0 3 6 1 cm 4 12 7 cm

A lamp is placed 6 0 m from a wall On putting a lens between the lamp and the wall at a distance of 1 2 m from the lamp a real image of the lamp is formed on the wall The magnification of the image is 1 3 2 4 3 5 4 6

5 Two convex and concave lens are in contact and having focal length 12 cm and 18 cm respectively Focal length of joint lens will be a 50 cm b 45 cm c 36 cm d 18 cm 6 Two lenses are kept in contact with powers 2D and 4D The focal length of this combination will be

19 Draw a labelled ray diagram of an astronomical telescope in the near point adjustment position 3 A giant refracting telescope at an observatory has an objective lens of focal length 15 m and an eyepiece of focal length 1 0 cm If this telescope is used to view the Moon find the diameter of the image of the Moon formed by the objective lens The diameter of the Moon is 3 48 x 106 m and the radius of lunar orbit is 3 8 x 108 m

combining 2 prisms as shown If o then A A is made by 2 1 Average deviation would be clockwise 2 Average deviation would be anticlockwise 3 Average deviation would be zero 4 Cannot be predicted on basis of given

6 Two lenses are kept in contact with powers 2D and 4D The focal length of this combination will be a 50 cm b 50 cm c 25 cm d 25 cm 2 7 the amount of scattering is inversly proportional to the fourth power of the wav This is known as

A ray of light travelling inside a rectangular glass block of refractive index 2 is incident on the glass air surface at an angle of incidence of 45 The refractive index of air is one Under these conditions the ray KEE 9 S 1 Will emerge into the air without any deviation 2 Will be reflected back into the glass 3 Will be absorbed 4 Will emerge into the air with an angle of refraction equal to 90

A point object is placed at a distance of 10 cm and its real image is formed at a distance of 20 cm from a concave mirror If the object is moved by 0 1 cm towards the mirror the image will shift by about Question Type Single Correct Type 1 0 4 cm away from the mirror 2 0 4 cm towards the mirror 3 0 8 cm away from the mirror 4 0 8 cm towards the mirror

5 A biprism is placed 10 cm from a slit illuminated by light of wavelength 5890 A The width of the fringes obtained on a screen at 80 cm from the biprism is 9 x102 cm What is the distance between the two coherent sources 3 marks 6 A telescope has an obiective of focal length 50 cms and eveniece of focal length 5cms The least distance

Example 53 An equiconvex lens of focal length 15 cm is cut into two equal halves as shown in Fig 9 72 What is the focal length of each half CBSE Sample Paper 98 Solution For the equiconvex lens let R R R R Then from lens maker s formula 1 12 1 1 R 1 f For each half lens R R R 00 7 7 4 1 12 13 1 201 1 f R f 1 f 2 x 15 30 cm Dividing i by ii we get 2 u 1 isol R 1 1 R 2 1 Fig 9 72 i ve why ii

A point object approaches a plane mirror with a speed of 10 ms while the image recedes away from the mirror with a speed of 6 ms The direction and magnitude of the velocity of mirror is 1 towards the object 8 ms 2 towards the image 6 ms 3 away from the object 8 ms from the obiect ms

me 10 An object AB is placed parallel and close to the optical axis between focus F and centre of curvature C of a converging mirror of focal length f as shown in figure imponent Colouss of white light at a single c ATB F Jonline mir 1 Image of B will be closer than that of A from the mirror 2 Image of AB will be parallel to the optical axis 3 Length of image is equal to AB 4Length of image is more than AB

of their de Broglie wavelengths 23 Calculate the radius of curvature of a equi concave lens of refractive index 1 5 when it is kept in a medium of refractive index 1 4 to have a power of 5D 24 Identify the electromagnetic waves whose wavelengths vary as

37 180 A convex mirror of focal length F is placed at distance x from a convex lens of focal length F A beam of light from infinity falls on convex lens convex mirror combination and returns to infinity the distance x must be F F and F x

7 An object O is kept in air in front of a thin plano convex lens of radius of curvature 10cm It s refractive index is 3 1 5cm 3 20cm 2 and medium towards right of 4 plane surface is water of refractive index should be the distance x of the object so that the rays become parallel finally I 3 2 10cm 4 None of these What

Two identical glass 3 2 equiconvex lenses of focal length f each are kept in contact The space between the two lenses is filled with water Hw 4 3 The focal length of the combination is 1 Af 3 2 36 A 2 3 4 f

4 A transparent rod 40 cm long is cut flat at one end and rounded to a hemispherical surface of 12 cm radius at the other end A small object is embedded within the rod on its axis half way between its ends When viewed from the flat end of the rod the apparent depth of the object is 12 5 cm What is the apparent depth when viewed from from the curved end

A ray of light moving parallel to x axis is incident on a parabolic mirror at point P as shown in figure If angle of deviation suffered by the ray after reflection is 120 the y coordinate of point P is y 3x 1 3 2 3 1 P is 2 3 1 00 4 1 4

5 A ray is incident on prism at an angle i with normal When it comes out of prism its angular deviation is 8 Graph between 8 and i is given Find the prism angle VERA to 2 20 A 8 10 5 20 38 Ans 48

5 A convex lens of focal length 20 cm is used to form a real image of an object placed 35 cm away from the lens Where should a convex mirror of focal length 10 cm be placed such that the final image coincides with the object

Two prisms of same glass u 2 are stuck together without gap as shown Find the angle of incidence i on the face AC such that the deviation produced by the combination is minimum MOC 31 1 60 3 30 181 A C70 ro0iphol les 20 and 60 40 B 2 15 4 45 A

A screen is at a distance D 80 cm from a diaphragm having two narrow slits S and S which are d 2 mm apart Slit S is covered by a transparent sheet of thickness 1 2 5 m and slit S is covered by another sheet of thickness 1 25 m as shown in figure S S C Both sheets are made of same material having refractive index 1 40 Water is filled in the space between diaphragm and screen A monodichromatic light beam of wavelength 5000 is incident normally on the diaphragm Assuming intensity of beam to be uniform calculate ratio of intensity of C to maximum intensity of interference pattern obtained on the screen u 4 3

A thin biconvex lens of refractive index 3 2 is placed on a horizontal plane mirror as shown The space between the lens and the mirror is then filled with water of refractive index 4 3 It is found that when a point object is placed 15cm above the lens on its principal axis the object coincides with its own images On representing with another liquid the object and the image again coincide at a distance 25cm from the lens Calculate if the refractive index of the liquid is

A concavo convex lens made of glass 1 5 has surfaces of radii 20 cm and 60 cm The nature and position of image of an object placed 80 cm to the left of lens is L 0 80cm A real 240 cm to the right of the lens C virtual 240 cm to the right of the lens B real 240 cm to the left of the lens D virtual 240 cm to the left of the lens

is placed over a plane mirror as shown then object needle and its image coincide at 15 cm When a liquid of refractive index is filled in the gap between mirror and lens the object needle and its image coincide at 40 cm

A plano convex lens with a radius of curvature R is lying on a reflecting plane surface such that the convex part of the lens is in contact with the plane surface The lens is illuminated from above The shape of interference fringes is A circular B hyperbolic C elliptical D parabolic Fifty one tuning forks are arranged in order of increasing frequencies so that each fork gives 3 beats per second

The graph between object distance u and image distance v for a lens is given below The focal length of the lens is 2006 3M a 5 0 1 05 01 11 10 45 9 10 11 9 b 5 0 05 d 0 5 0 05

1 2 sin A 2 2 cos A 4 tanA 50 A ray falls on a prism ABC on 3 AB BC and travels as shown in figure The minimum refractive index of the prism material should be 90 2 2 3 1 5 4 3 1 60 2 REFRACTION AT 55 A point object having spherica The image wou 15 1 30 cm left 3 1 cm to the

Reflection at Curved Surface 3 A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such way that the end farther from the pole is 20 cm away from it Find the length of the image A concave mirror of focal length 20 cm is cut into two parts from the middle and 4 orto pro

08 Two plane mirrors are placed as shown in the figure Object 0 0 1 1 25 2 4 2 3 2 2 2 2 2 0 a How many images will be formed b Find the position s of image s c Will the ray passing through 1 1 25 take part in image formation

The refractive indices of the material of a prism for red and violet colours are 1 72 and 1 75 respectively Determine the angular dispersion and dispersive power if refracting angle of prism is 6