geometrical optics 95

GEOMETRICAL OPTICS

PHYSICS

C O N T E N T S

OBJECTIVE QUESTION BANK.................................. Page –2

ANSWER KEY ............................................................... Page –28

By N.K.C. SIR

(QUESTION BANK)

Geometrical Optics [2]

OBJECTIVE QUESTION BANKONLY ONE OPTION IS CORRECT.

Take approx. 2 minutes for answering each question.

Q.1 Two plane mirrors are inclined at 70º. A ray incident on one mirror at angleafter reflection falls on thesecond mirror and is reflected from there parallel to the first mirror, is :(A) 50º (B) 45º (C) 30º (D) 55º

Ans.

Q.2 There are two plane mirror with reflecting surfaces facing each other. Both the mirrors are moving withspeed v away from each other. A point object is placed between the mirrors. The velocity of the imageformed due to n-th reflection will be(A) nv (B) 2nv (C) 3nv (D) 4nv

Ans.

Q.3 A man of height ‘h’ is walking away from a street lamp with a constant speed ‘v’. The height of the streetlamp is 3h. The rate at which of the length of the man’s shadow is increasing when he is at a distance 10hfrom the base of the street lamp is :(A) v/2 (B) v/3 (C) 2v (D) v/6

Ans.

Q.4 A boy of height 1.5 m with his eye level at 1.4 m stands before a plane mirror of length 0.75 m fixed onthe wall. The height of the lower edge of the mirror above the floor is 0.8 m. Then :(A) the boy will see his full image (B) the boy cannot see his hair(C) the boy cannot see his feet (D) the boy cannot see neither his hair nor his feet.

Ans.

Q.5 A point source of light S is placed in front of two large mirrors as shown. Whichof the following observers will see only one image of S?(A) only A (B) only C(C) Both A and C (D) Both B and C

Ans.


Q.6 The reflecting surface of a plane mirror is vertical. A particle is projected in a vertical plane which is alsoperpendicular to plane of the mirror. The initial velocity of the particle is 10 m/s and the angle of projectionis 60°. The point of projection is at a distance 5 m from the mirror. The particle moves towards themirror. Just before the particle touches the mirror the velocity of approach of the particle and its image is:

(A) 10 m/s (B) 5 m/s (C) 310 m/s (D) 35 m/sAns.

Q.7 The circular boundary of the concave mirror subtends a cone of half angle atits centre of curvature. The minimum value of for which ray incident on thismirror parallel to the principle axis suffers more than one reflection is(A) 30° (B) 45° (C) 60° (D) 75°

Ans.

Q.8 The passenger side-view mirror on an automobile often has the notation. "Objects seen in mirror arecloser than they appear". Is the image really farther away than the object?(A) Yes, the image is smaller and farther away than the object(B) No, the image is smaller and closer than the object(C) No, the image is larger and closer than the object(D) Yes, the image is larger and farther away than the object

Ans.

Q.9 In the figure shown, the image of a real object is formed at point I.AB is the principal axis of the mirror. The mirror must be :(A) concave & placed towards right I(B) concave & placed towards left of I(C) convex and placed towards right of I(D) convex & placed towards left of I.

Ans.


Q.10 A straight line joining the object point and image point is always perpendicular to the mirror(A) if mirror is plane only (B) if mirror is concave only(C) if mirror is convex only (D) irrespective of the type of mirror.

Ans.

Q.11 An object is placed in front of a convex mirror at a distance of 50 cm. A plane mirror is introduced covering thelower half of the convex mirror. If the distance between the object and the plane mirror is 30 cm, it is found thatthere is no gap between the images formed by the two mirrors. The radius of the convex mirror is :(A) 12.5 cm (B) 25 cm (C) 50 cm (D) 100 cm

Ans.

Q.12 An infinitely long rod lies along the axis of a concave mirror of focal length f. The near end of the rod isat a distance u > f from the mirror. Its image will have a length(A) f 2/(u–f) (B) uf / (u–f) (C) f 2 /(u + f) (D) uf /(u + f)

Ans.

Q.13 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 towards the mirror (B) 6 away from the mirror(C) 9 away from the mirror (D) 9 towards the mirror

Ans.

Q.14 In the figure shown if the object ‘O’ moves towards the plane mirror, then the imageI (which is formed after successive reflections from M1 & M2 respectively)will move:(A) towards right (B) towards left(C) with zero velocity (D) cannot be determined

Ans.


Q.15 A point source of light is 60 cm from a screen and is kept at the focus of a concave mirror which reflectslight on the screen. The focal length of the mirror is 20 cm. The ratio of average intensities of the illuminationon the screen when the mirror is present and when the mirror is removed is :(A) 36 : 1 (B) 37 : 1 (C) 49 : 1 (D) 10:1

Ans.

Q.16 A ray of sunlight enters a spherical water droplet (n = 4/3) at an angle of incidence 53° measured withrespect to the normal to the surface. It is reflected from the back surface of the droplet and re-enters intoair. The angle between the incoming and outgoing ray is [Take sin 53° = 0.8](A) 15° (B) 34° (C) 138° (D) 30°

Ans.

Q.17 A ray of light moving along the unit vector (– i – 2j) undergoes refraction at an interface of two media,

which is the x-z plane. The refractive index for y > 0 is 2 while for y < 0, it is 25 . The unit vector along

which the refracted ray moves is :

(A)34

)j5i3( (B)

5

)j3i4( (C)

5

)j4i3( (D) None of these

Ans.

Q.18 A bird is flying 3 m above the surface of water. If the bird is diving vertically down with speed = 6 m/s,his apparent velocity as seen by a stationary fish underwater is :(A) 8 m/s (B) 6 m/s (C) 12 m/s (D) 4 m/s

Ans.

Q.19 A parallel sided block of glass of refractive index 1.5 which is 36 mm thick rests on thefloor of a tank which is filled with water (refractive index = 4/3). The difference betweenapparent depth of floor at A & B when seen from vertically above is equal to(A) 2 mm (B) 3 mm (C) 4 mm (D) none of these

Ans.


Q.20 A beam of light is converging towards a point I. A planeparallel plate of glass of thickness t , refractive index is introduced in the path of the beam. The convergentpoint is shifted by (assume near normal incidence) :

(A)

11t away (B)

11t away

(C)

11t nearer (D)

11t nearer

Ans.

Q.21 A concave mirror is placed on a horizontal table, with its axis directed vertically upwards. Let O be thepole of the mirror and C its centre of curvature. A point object is placed at C. It has a real image, alsolocated at C (a condition called auto-collimation). If the mirror is now filled with water, the image will be:(A) real, and will remain at C (B) real, and located at a point between C and(C) virtual, and located at a point between C and O (D) real, and located at a point between C and O

Ans.

Q.22 In the diagram shown below, a point source O is placed vertically below the center of a circular planemirror. The light rays starting from the source are reflected from the mirror such that a circular area A onthe ground receives light. Now, a glass slab is placed between the mirror and the source O. What will themagnitude of the new area on the ground receiving light?(A) A(B) Greater than A(C) Less than A(D) Cannot tell, as the information given is insufficient

Ans.

Q.23 In the figure ABC is the cross section of a right angled prism and BCDE is thecross section of a glass slab. The value of so that light incident normally on theface AB does not cross the face BC is (given sin–1 (3/5) = 37°)(A) 37° (B) > 37° (C) 53° (D) < 53°

Ans.


Q.24 A small source of light is 4m below the surface of a liquid of refractive index 5/3. In order to cut off all thelight coming out of liquid surface, minimum diameter of the disc placed on the surface of liquid is :(A) 3m (B) 4m (C) 6m (D)

Ans.

Q.25 A point source of light is placed at a distance h below the surface of a large deep lake. What is thepercentage of light energy that escapes directly from the water surface? of the water = 4/3? (neglectpartial reflection)(A) 50% (B) 25% (C) 20% (D) 17%

Ans.

Q.26 A vertical pencil of rays comes from bottom of a tank filled with a liquid. When it is accelerated horizontallywith an acceleration of 7.5 m/s2, the ray is seen to be totally reflected by liquid surface. What is minimumpossible refractive index of liquid?(A) slightly greater than 4/3 (B) slightly greater than 5/3(C) slightly greater than 1.5 (D) slightly greater than 1.75

Ans.

Q.27 Two glass blocks of triangular cross section (n = 1.5) are used to make a periscope. Which of thefollowing is the correct arrangement?

(A) (B) (C) (D)

Ans.

Q.28 A ray of light from a denser medium strike a rarer medium. The angle of reflection is r and that of refractionis r'. The reflected and refracted rays make an angle of 90° with each other. The critical angle will be :(A) sin–1(tan r) (B) tan–1(sin r) (C) sin–1 (tan r') (D) tan–1 (sin r')

Ans.


Q.29 Consider a common mirage formed by super-heated air just above a roadway. A truck driver is in amedium of = 1.000 3 looks forward. He perceives the illusion of a patch of water ahead on the road,where his line of sight makes an angle of 1.20° below the horizontal. Find the index of refraction of the airjust above the road surface. (Hint: Treat this as a problem in total internal reflection.)(A) 1.00006 (B) 1.0001 (C) 1.00008 (D) None of these

Ans.

Q.30 A concave spherical surface of radius of curvature 10cm separates two mediumX & Y of refractive index 4/3 & 3/2 respectively. If the object is placed alongprincipal axis in medium X then(A) image is always real(B) image is real if the object distance is greater than 90cm(C) image is always virtual(D) image is virtual if the object distance is less than 90cm

Ans.

Q.31 A fish is near the centre of a spherical water filled ( = 4/3) fish bowl. A child stands in air at a distance2R (R is the radius of curvature of the sphere) from the centre of the bowl. At what distance from thecentre would the child nose appear to the fish situated at the centre :(A) 4R (B) 2R (C) 3R (D) 4R

Ans.

Q.32 A beam of diameter ‘d’ is incident on a glass hemisphere as shown. If the radiusof curvature of the hemisphere is very large in comparison to d, then the diameterof the beam at the base of the hemisphere will be:

(A)4

3 d (B) d (C)

3

d(D)

3

2 d

Ans.


Question No. 33 to 35 (3 questions)The figure, shows a transparent sphere of radius R and refractive index. Anobject O is placed at a distance x from the pole of the first surface sothat a real image is formed at the pole of the exactly opposite surface.

Q.33 If x = 2R, then the value of is(A) 1.5 (B) 2 (C) 3 (D) none of these

Ans.

Q.34 If x =, then the value of is(A) 1.5 (B) 2 (C) 3 (D) none of these

Ans.

Q.35 If an object is placed at a distance R from the pole of first surface, then the real image is formed at adistance R from the pole of the second surface. The refractive index of the sphere is given by

(A) 1.5 (B) 2 (C) 2 (D) none of theseAns.

Q.36 When the object is at distances u1 and u

2 the images formed by the same lens are real and virtual

respectively and of the same size. Then focal length of the lens is :

(A) 21uu2

1(B) )uu(

2

121 (C) 21uu (D) 2 (u

1 + u

2)

Ans.

Q.37 Parallel beam of light is incident on a system of two convex lenses of focallengths f

1 = 20 cm and f

2 = 10 cm. What should be the distance between the

two lenses so that rays after refraction from both the lenses pass undeviated :(A) 60 cm (B) 30 cm(C) 90 cm (D) 40 cm

Ans.


Q.38 An object is placed at a distance of 15 cm from a convex lens of focallength 10 cm. On the other side of the lens, a convex mirror is placed atits focus such that the image formed by the combination coincides withthe object itself. The focal length of the convex mirror is(A) 20 cm (B) 10 cm (C) 15 cm (D) 30 cm

Ans.

Q.39 A thin lens of focal length f and its aperture has a diameter d. It forms an image of intensity I. Now thecentral part of the aperture upto diameter (d/2) is blocked by an opaque paper. The focal length andimage intensity would change to(A) f/2, I/2 (B) f, I/4 (C) 3f/4, I/2 (D) f, 3I/4

Ans.

Q.40 An object is placed in front of a thin convex lens of focal length 30 cm and a plane mirror is placed 15 cmbehind the lens. If the final image of the object coincides with the object, the distance of the object fromthe lens is(A) 60 cm (B) 30 cm (C) 15 cm (D) 25 cm

Ans.

Question No. 41 to 43 (3 questions)A turnip sits before a thin converging lens, outside the focal point of thelens. The lens is filled with a transparent gel so that it is flexible; by squeezingits ends toward its center [as indicated in figure(a)], you can change thecurvature of its front and rear sides.

Ans.

Q.41 When you squeeze the lens, the image.(A) moves towards the lens (B) moves away from the lens(C) shifts up (D) remains as it is

Ans.


Q.42 When you squeeze the lens, the lateral height of image.(A) increases (B) decreases (C) remains same (D) data insufficient

Ans.

Q.43 Suppose that a sharp image must be formed on a card which is at a certaindistance behind the lens [figure(b)], while you move the turnip away fromthe lens, then you should(A) decrease the squeeze of the lens(B) increase the squeeze of the lens(C) keep the card and lens as it is.(D) move the card away from the lens

Ans.

Q.44 If an object is placed at A (OA>f); Where f is the focal length ofthe lens the image is found to be formed at B. A perpendicular iserected at O and C is chosen on it such that the angleBCA isa right angle. Then the value of f will be(A) AB/OC2 (B) (AC)(BC)/OC (C) (OC)(AB)/AC+BC (D) OC2/AB

Ans.

Q.45 The height of the image formed by a converging lens on a screen is 8cm. For the same position of theobject and screen again an image of size 12.5cm is formed on the screen by shifting the lens. The heightof the object :(A) 625/32cm (B) 64/12.5cm (C) 10cm (D) none

Ans.

Q.46 A converging lens of focal length 20 cm and diameter 5 cm is cut along theline AB. The part of the lens shown shaded in the diagram is now used toform an image of a point P placed 30 cm away from it on the line XY. Whichis perpendicular to the plane of the lens. The image of P will be formed.(A) 0.5 cm above XY (B) 1 cm below XY(C) on XY (D) 1.5 cm below XY

Ans.


Q.47 A screen is placed 90 cm from an object. The image of an object on the screen is formed by a convexlens at two different locations separated by 20 cm. The focal length of the lens is(A) 18 cm (B) 21.4 cm (C) 60 cm (D) 85.6 cm

Ans.

Q.48 In the above problem, if the sizes of the images formed on the screen are 6 cm and 3 cm, then the heightof the object is nearly :(A) 4.2 cm (B) 4.5 cm (C) 5 cm (D) 9 cm

Ans.

Q.49 Look at the ray diagram shown, what will be the focallength of the 1st and the 2nd lens, if the incident light rayis parallel to emergent ray.(A) –5cm and –10cm(B) +5cm and +10cm(C) –5cm and +5cm(D) +5cm and +5cm

Ans.

Q.50 A point object is kept at the first focus of a convex lens. If the lens starts moving towards right with aconstant velocity, the image will(A) always move towards right(B) always move towards left(C) first move towards right & then towards left.(D) first move towards left & then towards right.

Ans.

Q.51 Two planoconvex lenses each of focal length 10 cm & refractive index 3/2 areplaced as shown. In the space left, water (R.I = 4/3) is filled. The wholearrangement is in air. The optical power of the system is (in diopters) :(A) 6.67 (B) – 6.67 (C) 33.3 (D) 20

Ans.


Q.52 The curvature radii of a concavo-convex glass lens are 20 cm and 60 cm. The convex surface of the lensis silvered. With the lens horizontal, the concave surface is filled with water. The focal length of theeffective mirror is ( of glass = 1.5, of water = 4/3)(A) 90/13 cm (B) 80/13 cm (C) 20/3 cm (D) 45/8 cm

Ans.

Q.53 An object is placed in front of a symmetrical convex lens with refractive index 1.5 and radius of curvature40 cm. The surface of the lens further away from the object is silvered. Under auto-collimation condition,the object distance is(A) 20 cm (B) 10 cm (C) 40 cm (D) 5 cm

Ans.

Q.54 A planoconvex lens, when silvered at its plane surface is equivalent to a concave mirror of focal length28cm. When its curved surface is silvered and the plane surface not silvered, it is equivalent to a concavemirror of focal length 10cm, then the refractive index of the material of the lens is :(A) 9/14 (B) 14/9 (C) 17/9 (D) none

Ans.

Q.55 A beam of monochromatic light is incident at i =50° on one face of an equilateral prism, the angle ofemergence is 40°, then the angle of minimum deviation is :(A) 30° (B) < 30° (C) 30° (D) 30°

Ans.

Q.56 A ray incident at an angle 53° on a prism emerges at an angle at 37° as shown. If theangle of incidence is made 50°, which of the following is a possible value of the angleof emergence.(A) 35° (B) 42° (C) 40° (D) 38°

Ans.

Q.57 A prism has a refractive index2

3 and refracting angle 90°. Find the minimum deviation produced by prism.

(A) 40° (B) 45° (C) 30° (D) 49°Ans.


Q.58 A certain prism is found to produce a minimum deviation of 38°. It produces a deviation of 44° when the angleof incidence is either 42° or 62°. What is the angle of incidencewhen it is undergoing minimum deviation?(A) 45° (B) 49° (C) 40° (D) 55°

Ans.

Q.59 A thin prism of angle 5° is placed at a distance of 10 cm from object. What is the distance of the imagefrom object? (Given of prism = 1.5)

(A)8

cm (B)

12

cm (C)

36

5 cm (D)

7

cm

Ans.

Q.60 Light ray is incident on a prism of angle A = 60° and refractive index = 2 . The angle of incidence atwhich the emergent ray grazes the surface is given by

(A)

2

13sin 1

(B)

2

31sin 1

(C) sin–1

2

3(D) sin–1

3

2

Ans.

Q.61 When a monochromatic light ray is incident on a medium of refractive index with angle of incidencei , the angle of refraction isr. Ifi is changed slightly byi , then the corresponding change inr will be

(A) i (B) i (C) ir

i ·cos

cos·

1

(D)· ir

i ·sin

sin

Ans.

Q.62 Two lenses in contact made of materials with dispersive powers in the ratio 2 : 1, behaves as an achromaticlens of focal length 10 cm. The individual focal lengths of the lenses are:(A) 5 cm, –10 cm (B) – 5 cm, 10 cm (C) 10 cm, – 20 cm (D) – 20 cm, 10 cm

Ans.


Q.63 A beam of light consisting of red, green and blue is incident on a right angled prism. The refractive indexof the material of the prism for the above red, green and blue wavelengths are 1.39, 1.44 and 1.47respectively. The prism will :(A) separate part of the red color from the green and blue colors.(B) separate part of the blue color from the red and green colours.(C) separate all the three colors from the other two colors.(D) not separate even partially any color from the other two colors.

Ans.

Q.64 It is desired to make an achromatic combination of two lenses (L1 & L2) made of materials havingdispersive powers1 and2 (<1). If the combination of lenses is converging then(A) L1 is converging (B) L2 is converging(C) Power of L1 is greater than the power of L2 (D) None of these

Ans.

ASSERTION AND REASON

Q.1 Statement 1 : If a source of light is placed in front of rough wall its image is not seen.Statement 2 : The wall does not reflect light.(A) Statement-1 is true, statement-2 is true; statement-2 is correct explanation for statement-1.(B) Statement-1 is true, statement-2 is true; statement-2 is NOT the correct explanation for statement-1.(C) Statement-1 is true, statement-2 is false.(D) Statement-1 is false, statement-2 is true.

Ans.

Q.2 Statement 1 : As the distance x of a parallel ray from axis increases, focal length decreases

Statement 2 : As x increases, the distance from pole to the point of intersection of reflected ray with principal axis decreases

(A) Statement-1 is true, statement-2 is true; statement-2 is correct explanation for statement-1.(B) Statement-1 is true, statement-2 is true; statement-2 is NOT the correct explanation for statement-1.(C) Statement-1 is true, statement-2 is false.(D) Statement-1 is false, statement-2 is true.

Ans.


Q.3 Statement-1 : When an object dipped in a liquid is viewed normally, the distance between the imageand the object is independent of the height of the liquid above the object.Statement-2 : The normal shift is independent of the location of the slab between the object and theobserver.(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.(C) Statement-1 is true, statement-2 is false.(D) Statement-1 is false, statement-2 is true.

Ans.

Q.4 Statement-1 : When two plane mirrors are kept perpendicular to each other as shown (O is the pointobject), 3 images will be formed.

O

Statement-2 : In case of multiple reflection, image of one surface can act as an object for the nextsurface.(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.(C) Statement-1 is true, statement-2 is false.(D) Statement-1 is false, statement-2 is true.

Ans.

Q.5 Statement-1 : Keeping a point object fixed, if a plane mirror is moved, the image will definitely move.Statement-2 : In case of a plane mirror, distance of a point object and its image from a given point on

mirror is equal.(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.(C) Statement-1 is true, statement-2 is false.(D) Statement-1 is false, statement-2 is true.

Ans.


ONE OR MORE THAN ONE OPTION MAY BE CORRECTTake approx. 3 minutes for answering each question.Q.1 A man of height 170 cm wants to see his complete image in a plane mirror (while standing). His eyes are

at a height of 160 cm from the ground.(A) Minimum length of the mirror = 80 cm(B) Minimum length of the mirror = 85 cm.(C) Bottom of the mirror should be at a height 80 cm or less(D) Bottom of the mirror should be at a height 85 cm.

Ans.

Q.2 A flat mirror M is arranged parallel to a wall W at a distance l from it. The lightproduced by a point source S kept on the wall is reflected by the mirror and producesa light spot on the wall. The mirror moves with velocity v towards the wall.(A) The spot of light will move with the speed v on the wall.(B) The spot of light will not move on the wall.(C) As the mirror comes closer the spot of light will become larger and shift away from the wall with

speed larger then v.(D) The size of the light spot on the wall remains the same.

Ans.

Q.3 A reflecting surface is represented by the equation Y =

L

xsin

L2 , 0 x L. A ray travelling

horizontally becomes vertical after reflection. The coordinates of the point (s) where this ray is incident is

(A)

L2

,4

L (B)

L3

,3

L (C)

L2

,4

L3 (D)

L3

,3

L2

Ans.

Q.4 A concave mirror cannot form(A) virtual image of virtual object (B) virtual image of a real object(C) real image of a real object (D) real image of a virtual object.

Ans.


Q.5 In the figure shown consider the first reflection at the plane mirrorand second at the convex mirror. AB is object.(A) the second image is real , inverted of 1/5 th magnification w.r.t AB(B) the second image is virtual and erect with magnification1/5 w.r.t AB(C) the second image moves towards the convex mirror(D) the second image moves away from the convex mirror.

Ans.

Q.6 A ray of light is incident normally on one face of 30° – 60° – 90° prismof refractive index 5/3 immersed in water of refractive index 4/3 asshown in figure.

30°

1

2

P

(A) The exit angle2 of the ray is sin–1(5/8)

(B) The exit angle2 of the ray is sin–1( 345 )

(C) Total internal reflection at point P ceases if the refractive index of water is increased to 325 by

dissolving some substance.(D) Total internal reflection at point P ceases if the refractive index of water is increased to 5/6 by

dissolving some substance.Ans.

Q.7 Point A(0, 1) and B (12, 5) are object – image pair (one of the point acts as object and the other pointas image) x-axis is the principal axis of the mirror. Then this object image pair is:(A) due to a convex mirror of focal length 2.5 cm(B) due to a concave mirror having its pole at (2, 0)(C) real virtual pair(D) data is insufficient for options (A) and (B)

Ans.

Q.8 A ray of light in a liquid of refractive index 1.4, approaches the boundary surface between the liquid andair at an angle of incidence whose sine is 0.8. Which of the following statements is correct about thebehaviour of the light(A) It is impossible to predict the behavior of the light ray on the basis of the information supplied.(B) The sine of the angle of refraction of the emergent ray will less than 0.8.(C) The ray will be internally reflected(D) The sine of the angle of refraction of the emergent ray will be greater than 0.8.


Ans.

Q.9 The figure shows a ray incident at an angle i =/3. If the plot drawn shown the variation of | r – i | versus

2

1

= k, (r = angle of refraction)

(A) the value of k1 is 3

2(B) the value of 1 = /6

(C) the value of 2 = /3 (D) the value of k2 is 1Ans.

Q.10 In the figure shown a point object O is placed in air on the principal axis. Theradius of curvature of the spherical surface is 60 cm. If is the final image formedafter all the refractions and reflections.(A) If d1 = 120 cm, then the ‘If’ is formed on ‘O’ for any value of d2.(B) If d1 = 240 cm, then the ‘If’ is formed on ‘O’ only if d2= 360 cm.(C) If d1 = 240 cm, then the ‘If’ is formed on ‘O’ for all values of d2.(D) If d1 = 240 cm, then the ‘If’ cannot be formed on ‘O’.

Ans.

Q.11 In the diagram shown, a ray of light is incident on the interface between 1 and 2 atangle slightly greater than critical angle. The light suffers total internal reflection atthis interface. After that the light ray falls at the interface of 1 and 3, and again it suffers total internal reflection. Which of the following relations should hold true?

(A) 1 < 2 < 3 (B)22

21 >

23

(C)23

21 >

22 (D)

22

21 >

23

Ans.


Q.12 Two refracting media are separated by a spherical interface as shown in the figure. PP’ is the principalaxis,1 and2 are the refractive indices of medium of incidence and medium of refraction respectively.Then :(A) if 2 > 1, then there cannot be a real image of real object.(B) if2 > 1, then there cannot be a real image of virtual object.(C) if1 >2, then there cannot be a virtual image of virtual object.(D) if 1 > 2, then there cannot be a real image of real object.

Ans.

Q.13 A luminous point object is placed at O, whose image is formed at I as shown in the figure. AB is theoptical axis. Which of the following statements are correct?(A) If a lens is used to obtain image, the lens must be converging(B) If a mirror is used to obtain image, the mirror must be a convex mirror

having pole at the point of intersection of lines OI and AB(C) Position of principal focus of mirror cannot be found(D) I is real image

Ans.

Q.14 A lens is placed in the XYZ coordinate system such that its optical center is at the origin and principalaxis is along the X axis. The focal length of the lens is 20 cm. A point object has been placed at the point(– 40 cm, + 1cm, –1 cm). Which of the following are correct about coordinates of the image?(A) x = 40 cm (B) y = + 1 cm (C) z = + 1 cm (D) z = – 1 cm

Ans.

Q.15 Which of the following can form diminished, virtual and erect image of your face.(A) Converging mirror (B) Diverging mirror (C) Converging lens (D) Diverging lens

Ans.


Q.16 A convex lens forms an image of an object on a screen. The height of the image is 9 cm. The lens is nowdisplaced until an image is again obtained on the screen. The height of this image is 4 cm. The distancebetween the object and the screen is 90cm.(A) The distance between the two positions of the lens is 30cm.(B) The distance of the object from the lens in its first position is 36cm.(C) The height of the object is 6cm.(D) The focal length of the lens is 21.6 cm.

Ans.

Q.17 A thin lens with focal length f is to be used as a magnifying glass. Which of the following statementsregarding the situation is true?(A) A converging lens may be used, and the object be placed at a distance greater than 2f from the lens.(B) A diverging lens may be used, and the object be placed between f and 2f from the lens.(C) A converging lens may be used, and the object be placed at a distance less than f from the lens.(D) A diverging lens may be used, and the object be placed at any point other than the focal point.

Ans.

Q.18 A man wanted to get a picture of a Zebra. He photographed a white donkey after fitting a glass withblack streaks onto the objective of his camera.(A) the image will look like a white donkey on the photograph.(B) the image will look like a Zebra on the photograph.(C) the image will be more intense compared to the case in which no such glass is used.(D) the image will be less intense compared to the case in which no such glass is used.

Ans.

Q.19 For refraction through a small angle prism, the angle of deviation :(A) increases with the increase in R.I. of prism.(B) will decrease with the increase in R.I. of prism.(C) is directly proportional to the angle of prism.(D) will be 2D for a ray of R.I.=2.4 if it is D for a ray of R.I.=1.2

Ans.


Q.20 For the refraction of light through a prism(A) For every angle of deviation there are two angles of incidence.(B) The light travelling inside an equilateral prism is necessarily parallel to the base when prism is set for

minimum deviation.(C) There are two angles of incidence for maximum deviation.(D) Angle of minimum deviation will increase if refractive index of prism is increased keeping the outside

medium unchanged ifP >S.Ans.

SUBJECTIVE

Q.1 Two flat mirrors have their reflecting surfaces facing each other, with an edge of one mirror in contactwith an edge of the other, so that the angle between the mirrors is 60° . Find all the angular positions ofthe image with respect to x-axis. Take the case when a point object is between the mirrors at (1, 1).Point of intersection is (0, 0) and 1st mirror is along x axis.

Ans.

Q.2 In figure shown AB is a plane mirror of length 40cm placed at a height 40cmfrom ground. There is a light source S at a point on the ground. Find the minimumand maximum height of a man (eye height) required to see the image of the source if he is standing at a point P on ground shown in figure.

A

B

40cm

40cm

20cm 40cm

S P

Ans.

Q.3 A plane mirror of circular shape with radius r = 20 cm is fixed to the ceiling. A bulb is to be placed on theaxis of the mirror. A circular area of radius R = 1 m on the floor is to be illuminated after reflection of lightfrom the mirror. The height of the room is 3m. What is maximum distance from the center of the mirrorand the bulb so that the required area is illuminated?

Ans.


Q.4 A concave mirror of focal length 20 cm is cut into two parts from themiddle and the two parts are moved perpendicularly by a distance 1 cmfrom the previous principal axis AB. Find the distance between theimages formed by the two parts?

Ans.

Q.5 A balloon is rising up along the axis of a concave mirror of radius of curvature 20 m. A ball is droppedfrom the balloon at a height 15 m from the mirror when the balloon has velocity 20 m/s. Find the speedof the image of the ball formed by concave mirror after 4 seconds? [Take : g=10 m/s2]

Ans.

Q.6 A thin rod of length d/3 is placed along the principal axis of a concave mirror of focal length = d such thatits image, which is real and elongated, just touches the rod. Find the length of the image?

Ans.

Q.7 A point object is placed 33 cm from a convex mirror of curvature radius = 40 cm. A glass plate ofthickness 6 cm and index 2.0 is placed between the object and mirror, close to the mirror. Find thedistance of final image from the object?

Ans.

Q.8 A large temple has a depression in one wall. On the floor plan it appears as a indentation having sphericalshape of radius 2.50 m. A worshiper stands on the center line of the depression, 2.00 m out from itsdeepest point, and whispers a prayer. Where is the sound concentrated after reflection from the backwall of the depression?

Ans.


Q.9 An opaque cylindrical tank with an open top has a diameter of 3.00 m and is completely filled with water.When the setting Sun reaches an angle of 37° above the horizon, sunlight ceases to illuminate any part ofthe bottom of the tank. How deep is the tank?

Ans.

Q.10 A beam of parallel rays of width b propagates in glass at an angle to itsplane face . The beam width after it goes over to air through this face is_______ if the refractive index of glass is

Ans.

Q.11 A room contains air in which the speed of sound is 340 m/s. The walls of the room are made of concrete,in which the speed of sound is 1 700 m/s. (a) Find the critical angle for total internal reflection of soundat the concrete–air boundary. (b) In which medium must the sound be traveling to undergo total internalreflection?

Ans.

Q.12 A rod made of glass ( = 1.5) and of square cross-section is bent into the shapeshown in figure. A parallel beam of light falls perpendicularly on the plane flat surfaceA. Referring to the diagram, d is the width of a side & R is the radius of inner

semicircle. Find the maximum value of ratioR

dso that all light entering the glass

through surface A emerge from the glass through surface B.Ans.

Q.13 A prism of refractive index 2 has a refracting angle of 30°. One of the refracting surfaces of the prismis polished. For the beam of monochromatic light to retrace its path, find the angle of incidence on therefracting surface.

Ans.


Q.14 An equilateral prism deviates a ray through 23° for two angles of incidence differing by 23°. Find of the prism?Ans.

Q.15 A ray is incident on a glass sphere as shown. The opposite surface of thesphere is partially silvered. If the net deviation of the ray transmitted at thepartially silvered surface is 1/3rd of the net deviation suffered by the rayreflected at the partially silvered surface (after emerging out ofthe sphere). Find the refractive index of the sphere.

Ans.

Q.16 Anarrowparallel beam of light is incident on a transparent sphere of refractive index 'n'. If the beam finally getsfocussed at a point situated at a distance = 2×(radius of sphere) from the centre of the sphere, then find n?

Ans.

Q.17 A point object is placed at a distance of 25 cm from a convex lens of focal length 20 cm. If a glass slabof thickness t and refractive index 1.5 is inserted between the lens and object. The image is formed atinfinity. Find the thickness t ?

Ans.

Q.18 An object is kept at a distance of 16 cm from a thin lens and the image formed is real. If the object is keptat a distance of 6 cm from the same lens the image formed is virtual. If the size of the image formed areequal, then find the focal length of the lens?

Ans.


Q.19 A thin convex lens forms a real image of a certain object ‘p’ times its size. The size of real image becomes‘q’ times that of object when the lens is moved nearer to the object by a distance ‘a’ find focal length ofthe lens?

Ans.

Q.20 In the figure shown, the focal length of the two thin convex lenses isthe same = f. They are separated by a horizontal distance 3f andtheir optical axes are displaced by a vertical separation 'd' (d << f),as shown. Taking the origin of coordinates O at the centre of the firstlens, find the x and y coordinates of the point where a parallel beamof rays coming from the left finally get focussed?

Ans.

Q.21 A point source of light is kept at a distance of 15 cm from a converging lens, on its optical axis. The focallength of the lens is 10 cm and its diameter is 3 cm. A screen is placed on the other side of the lens,perpendicular to the axis of lens, at a distance 20 cm from it. Then find the area of the illuminated part ofthe screen?

Ans.

Q.22 A double convex lens has focal length 25.0 cm in air. The radius of one of the surfaces is double of theother. Find the radii of curvature if the refractive index of the material of the lens is 1.5.

Ans.

Q.23 A plano convex lens (=1.5) has a maximum thickness of 1 mm. If diameter of its aperture is4 cm. Find (i) Radius of curvature of curved surface; (ii) its focal length in air.

Ans.


Q.24 The refractive indices of the crown glass for violet and red lights are1.51 and 1.49 respectively and those of the flint glass are 1.77 and 1.73respectively. A prism of angle 6° is made of crown glass. A beam ofwhite light is incident at a small angle on this prism. The other thin flintglass prism is combined with the crown glass prism such that the netmean deviation is 1.5° anticlockwise.

(i) Determine the angle of the flint glass prism.(ii) A screen is placed normal to the emerging beam at a distance of 2m from the prism combination. Find

the distance between red and violet spot on the screen. Which is the topmost colour on screen.Ans.

Q.25 A prism of refractive index n1 & another prism of refractive index n

2

are stuck together without a gap as shown in the figure. The anglesof the prisms are as shown . n

1 & n

2 depend on , the wavelength of

light according to n1 = 1.20 + 2

4108.10

& n2 = 1.45 + 2

41080.1

where is in nm.(i) Calculate the wavelength

0 for which rays incident at any angle on the interface BC pass through

without bending at that interface .(ii) For light of wavelength

0, find the angle of incidence i on the face AC such that the deviation produced

by the combination of prisms is minimum .Ans.


OBJECTIVE QUESTION BANKONLY ONE OPTION IS CORRECT.

Q.1 A Q.2 B Q.3 A Q.4 C Q.5 B

Q.6 A Q.7 B Q.8 B Q.9 B Q.10 D

Q.11 B Q.12 A Q.13 C Q.14 A Q.15 D

Q.16 C Q.17 B Q.18 A Q.19 B Q.20 A

Q.21 D Q.22 A Q.23 A Q.24 C Q.25 D

Q.26 B Q.27 D Q.28 A Q.29 C Q.30 C

Q.31 C Q.32 D Q.33 C Q.34 B Q.35 B

Q.36 B Q.37 B Q.38 B Q.39 D Q.40 B

Q.41 A Q.42 B Q.43 A Q.44 D Q.45 C

Q.46 D Q.47 B Q.48 A Q.49 C Q.50 D

Q.51 A Q.52 A Q.53 A Q.54 B Q.55 B

Q.56 D Q.57 C Q.58 B Q.59 C Q.60 A

Q.61 C Q.62 A Q.63 A Q.64 B

ASSERTION AND REASON

Q.1 C Q.2 D Q.3 D Q.4 D Q.5 D

ONE OR MORE THAN ONE OPTION MAY BE CORRECT

Q.1 B, C Q.2 B, D Q.3 B, D Q.4 A Q.5 B, C

Q.6 A, C Q.7 B, C, D Q.8 C Q.9 B, C, D Q.10 A, B

Q.11 B, C, D Q.12 A, C Q.13 A, D Q.14 A, C Q.15 B, D

Q.16 B, C, D Q.17 C Q.18 A, D Q.19 A, C Q.20 B,C,D

SUBJECTIVE

Q.1 (i) 75° (ii) 165° (iii) 195° (iv) 285° (v) 315° Q.2 160cm; 320cm

Q.3 75 cm Q.4 2 cm Q.5 80 m/s Q.6 d/2

Q.7 42 cm Q.8

m

3

10Q.9 4m Q.10

sin

)cos1(b 2/122

Q.11 (a) sin–1

5

1 (b) air Q.12

maxR

d

=12 Q.13 45° Q.14

5

43

Q.15 3 Q.16 4/3 Q.17 15 cm Q.18 11 cm

Q.19 )pq(

apq

Q.20 (5f, 2d) Q.21 (/4) cm2 Q.22 75/4 cm, 75/2 cm

Q.23 (i) 0.2 m ,(ii) 0.4 m Q.24 (i) 2° ,(ii) mm9

4

Q.25 (i) 0 = 600 nm, n = 1.5 (ii) i = sin1 (0.75) = 48.59º

geometrical optics 95

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