Geometrical Optics Questions and Answers

A 4L u B u In the figure shown a thin parallel beam of light is incident on a plane mirror m at small angle 0 m is a concave mirror of focal length f After three successive reflections of this beam the x and y coordinates of the image is 16JP120294 A x f d y fe B x d f y fe D x d f y fe C x f d y fe m STATI A St B St

6 A thin lens is made in the shape of a disc of thickness d and radius R The refractive index u of material of disc varies with distance r from the centre If parallel beam of light get focused at distance f R from the lens then refractive index at centre of disc is 1 sip 3 r 2df r d f 2 4 F r 2df 2 r

1 A far sighted person can see object beyond 49 cm clearly If separation between glasses and eye lens is 1 cm then find focal length of glass 1 30 cm 2 25 cm 3 24 cm 4 48 cm

57 The right angled prisms of retr indices and are fitted together as shown in the fig 2 67 If a ray passes through the prisms without suffering any devaiation then find the relation between the three refractive indices of the prism D B 1 4 4 B E 2 1 4

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 refractive indices n and n n as shown in the figure A ray of light is incident with angle 0 from medium 1 and emerges in medium 2 with refraction angle 0 with a lateral displacement I Which of the following statement s is are true A n sino n sine C I is independent of n n constant z V n 2 n constant 0 1 2 Or B n sine n n sine D I is dependent on n z

Solution i Radius of curved surface of a plano convex lens is 20 cm and refractive index of lens material is 1 5 Calculate equivalent focal length of lens if i curved surface is silvered ii plane surface is silvered P 2P PM 2 1 R P P 2 R P f 20 2 R 2x1 5 2x1 5 1 20 f 20 cm BEGINNER S BOX 7 Please Solve by In the displacement method the distanco hotupon the shift P 2P PM P 2 1 1 R P 2 1 R 8 1 1 1 2 P R 20 2 1 2 1 5 1 quadratic method 20cm in 70 cm and the focal length ofa

At what two distances could you place an object from a 45 cm focal length concave mirror to get an image 1 5 times the object s size

4 mirror with the Figure sh equation of a section on the XY plane a y 4ax A light ray parallel to the X axis is incident on the mirror at a point with abscissa 4a The unit vector along the reflected ray is YA 0 1 41 3 M X

1 You are asked to design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm The radius of curvature of the mirror would then be 1 2 3 4 30 cm 24 cm 60 cm 24 cm

Q 4 Which factors determine the focal length of a lens Ans The focal length of a lens depends on i radii of curvature of the surfaces of the lens ii nature of matrial of the lens iii nature of medium in which lens is placed

III MATCH THE COLUMN A small particle is placed at the pole of a concave mirror and then moved along the principal axis to a large distance During the motion the distance between the pole of the mirror and the image measured The procedure is then repeated with a convex mirror a concave lens and a convex len The graph is plotted between image distance versus object distance Match the curves shown in th graph with the mirror or lens that is corresponding to it Curve 1 has two segments Lens Mirror A Converging lens B Converging Mirror C Diverging Lens D Diverging Mirror Image Distance Object Distance 3 2 Curve p 1 q 2 r 3 s 4

26 A concave mirror and a converging lens glass with 1 5 both have a focal length of 3 cm when in air When they are in water 3x2x4 3x3 their new focal lengths are a Lens 12 cm fMinor 3cm b fLens 3 cm fMirror 12cm c fLens 3 cm fMirror 3cm d fLens 12 cm fMirror 12cm 11 5x8

1 The refractive indices for violet and red colour are 1 54 and 1 52 respectively the angular dispersion of a prism of angle 20 and made of such glass will be A 0 4 C 3 06 B 0 2 D 30 6 quilateral prism minimum deviation is 30 what will be the angle of incidence

A convex lens of focal length 15 cm is split into two halves and the two halves are placed at separation of 120 cm Between the two halves of convex lens a plane mirror is placed horizonta and at a distance of 4 mm below the principal axis of the lens halves An object AB of length mm is placed at a distance of 20 cm from one half lens as shown in figure The final image of t point A is formed at a distance of mm from the principle axis Determine the value of n 3 f 15 cm f 15 cm 2 mm A B 20 cm 120 cm 4 mm

Light enters at an angle of incidence transparent rod of refractive index n For what value of the refractive index of the material of the rod the light once entered into it will not leave it through its lateral face whatsoever be the value of angle of incidence 1 n 1 1 2 n 1 3 n 2

18 3 equal to that of glass 4 less than one AIPMT Mains 2012 A rod of length 10 cm lies along the principal a of a concave mirror of focal length 10 cm in su a way that its end closer to the pole is 20 cm au from the mirror The length of the image is 1 2 5 cm 2 5 cm 3 10 cm 4 15 cm

8 An achromatic convergent doublet of two lenses in contact has a power of 2D The convex lens has a power 5D What is the ratio of the dispersive powers of the convergent and divergent lenses local noriv 1 2 5 2 3 5 3 5 2 4 5 3

The refractive index of glass is Ifa ray of light 2 travels 9 cm in glass medium find the distance it travels in air during the same time 2 1 35 cm 4 0 135 cm 1 13 5 cm 3 135 cm

Two identical thin plano convex glass lenses refractive index 1 5 each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre The intervening space is filled with oil of refractive index 1 7 The focal length of the combination is 1 25 cm 3 50 cm 2 50 cm 4 20 cm

For which of the following angle between two plane mirrors the incident ray and reflected ray from t are parallel to each other for all angle of incidence 1 30 3 90 2 45 4 120

59 A real image is formed by a convex lens when it is cemented with a concave lens again the real image is formed The real image 1 shifts towards the lens system 2 shifts away from the lens sytem 3 remains in its original position 4 shifts to infinity

Four identical lenses are kept one beside the other on the same optical axis as shown in the figure The right surface of rightmost lens is silvered Focal length of each lens is 20 cm and radius of the silvered surface is 20 cm The focal length of the combined system is 30 00 2 2 cm 4 5 cm 1 2 cm 3 5 cm

18 An object moving at a speed of 5m s towards a concave mirror of focal length f 1m is at a distance of 9m The average speed of the image is a m s c 5 m s b m s 10 d 2 3 m s

An object is moving of water with a speed of 2 ms 1 and fish F is moving towards the surface with a speed of 5 ms 1 Find the speed of the object O as seen by fish 0 2 ms 5 m s 1 6 33 ms 1 2 7 ms 1 3 5 26 ms 1 F H 2 H 4 3

An air bubble is inside the water water Which of the following is correct 1 It will behave like a divergent lens 2 It cannot form a real image of any point object in water 3 It can produce real image of virtual object 4 All of these 4 3

A parallel beam of light enters a convex lens of focal length 50 cm A concave lens of focal length 20 cm is kept coaxially at a distance D behind the convex lens such that rays coming out of concave lens are parallel again Here the D is equal to 1 20 cm 2 30 cm 3 40 cm 4 80 cm

of uniform thickness and refractive index n 1 4 is coated on convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index n 1 5 as shown in figure Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at a distance f from the film while rays of light travelling from glass to air get focused at a distance f from the film then coating air 1 f 3R 3 f 3R n n cylinder 2 f 2R 4 f 1 4R

An equiconvex lens of glass of focal length 0 1 m is cut along a plane perpendicular to principal axis into two equal parts The focal lengths of new lenses are 1 10 cm 10 cm 3 10 cm 10 cm BAG 2 20 cm 20 cm 4 5cm 5cm

If the angle of deviation by a plane mirror is 120 for a ray incident on it then the angle made by the incident ray with the mirror is 1 60 2 45 4 90 3 75

An equi convex lens whose focal length in air is 20cm is made up of a material whose refractive index is 1 5 If one of its surface is silvered and then dipped into transparent liquid whose refractive index is 1 6 In the liquid it will behave like a 1 converging lens 3 converging mirror Check all that apply A B C 2 diverging lens 4 diverging mirror

A light beam is traveling from Region I to Region IV Refer Figure The refractive index in no no Regions I II III and IV are no 6 and no 2 8 respectively The angle of incidence 0 for which the beam just misses entering Region IV in figure Region III Region IV Region I Region II D no 0 1 sin 3 sin nd 2 0 4 4 0 2 m no 6 2 sin 4 sin 0 6 m 8 3 no 8

index 1 50 Figure contact with a liquid layer on top of a plane mirror A small needle inverted image is found at the position of the needle The distance of with its tip on the principal axis is moved along the axis until the needle from the lens is measured to be 45 0 cm The liquid is removed and the experiment is repeated The new distance is measured to be 30 0 cm What is the refractive index of the liquid P P 9 y 45 y y

15 A small object is placed 20 cm in front of a block of glass 10 cm thick and its farther side silvered The image is formed 22 cm behind the silvered face Find the refractive index of glass 1 1 15 3 1 67 2 1 25 4 1 1

A luminous point object is placed at O whose image is formed at I as shown in figure Line AB is optic axis Which of the following statements are correct O 1 A a b B KBA b A If the lens is used to obtain the image the lens must be a converging lens and position of its principal focus can be found out B If the mirror is used to obtain the image the mirror must be a convex mirror whose pole will be at point of intersection of line OI with the optic axis C Position of principal focus of the mirror cannot be found out

The refractive index of material of a convex lens is changing with time as 1 x sin oot At 0 the focal length of the lens is f and Ho ao are constant a is very small A luminous poin object is placed on principal axis at a distance 3f from the optical centre The image appears to oscillate simple harmonically the amplitude of oscillation of image is 9af o A B 4 10 1 C 3af o 2 Ho 1 9af o 2 10 1 D none

The radius of curvature of spherical surfaces of a convex lens are 15 cm and 10 cm respectively If Refractive Index of lens is 1 5 then find its focal length

A flat mirror M is arranged parallel to a wall W at a distance L from it as shown in the figure The light produced by a point source S kept on the wall is reflected by the mirror and produces a light patch on the wall The mirror moves with velocity v towards the wall wall A B C D S V The patch of light will move with the speed v on the wall The patch of light will not move on the wall As the mirror comes closer the patch of light will become larger and shift away from the wall withspeed larger than v The width of the light patch on the wall remains the same

The minimum required size of plane mirror to visualize complete image of an object is 1 Half of size of object 2 Is same as size of object 3 Depends on distance of object only 4 Depends the ratio of distance of object and observer

s source 1m 4 A container is filled with water 3 upto height 1m Find out diameter of disc at top of water surface from which light is coming out 1 7 7m 2 7 m 3 m 45 3 A Z m

The angle of a prism is A One of its refracting surface is silvered Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silver surface The refractive index u of the prism is 1 2 sinA 2 2 cosA 1 3 COSA 4 tanA

59 A plano convex lenx u 1 5 has radius of curvature 10 cm It is silvered on its plane surface Find focal length after silvering 1 10 cm 2 20 cm 3 15 cm 4 25 cm

Monochromatic light is incident on a glass prism of angle A If the refractive index of the material of the prism is u a ray incident at an angle 0 on the face AB would get transmitted through the face AC of the prism provided 1 0 sin 1 0 usin A sin usin A sin A sin 1 3 0 cosusin A sin 2 0 cosusin A sin 1 05 14 Sin 01 usin A B 4 sinusin A sin 1 C 2015

An air bubble in a glass slab with refractive index 1 5 near normal incidence is 5 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face The thickness in cm of the slab is 1 12 2 16 3 8 4 10

A point source of light is place 4 m below the surface of water of refractive index 5 3 The minimum diameter of a disc which should be placed over the source on the surface of water to cut off all light coming out of water is 5 3 1 2 m 2 6 m 3 4 m 4 3 m

A bi convex lens is formed with two thin plan convex lenses as shown in the figure Refract index n of the first lens is 1 5 and that of second lens is 1 2 Both the curved surfaces are the same radius of curvature R 14 cm For bi convex lens for an object distance of 40 c the image distance will be n 1 5 n 1 2 R 14 cm

0 How many images will be formed if two mirrors are fitted on adjacent walls and one mirror on roof JMI 2001 AFMC 2002 a 2 c 7 b 5 0 10

cylindrical rod has a refractive index of 2 3 It is surrounded by air A light ray is incident at the midpoint of one end of the rod as shown in the figure soli The incident angle 0 for which the light ray grazes along the wall of the rod is 1 sin 1 2 2 sin 2 2 3 sin 2 3 165

5 A spherical surface of radius of curvature R separates air refractive index 1 0 from glass refractive index 1 5 The centre of curvature is in glass A point object P placed in air is found to have a real image Q in the glass The line PQ cuts the surface at a point O and PO OQ The distance PO is equal to 1 R 2 3 R 3 2 R 4 5 R

Two tree are at distance of 3 14 m from each other What should the maximum distance of an observer from tree to see them separately 1 21 6 km 2 10 8 km 3 15 km 4 25 2 km

27 at a distance of 60 m from the front of a tower the top of the tower and its image in the mirror subtend an angle of 90 at the eye The height of the tower is a 30 m b 60 m d 120 m c 90 m