8.OPTICS

OPTICS

DHANALAKSHMI NAGAR

NEAR ANNAMAIAH CIRCLE,

TIRUPATI.

Review of Concepts

(a) Due to reflection, none of frequency, wavelength and speed of light change.

(B) Law of reflection :

(i) Incident ray, reflected ray and normal on inident point are coplanar. (ii) The angle of incidence is equal to angle of reflection.

Some important points : In case of plane mirror :

(i) For real object, image is virtual. (ii) For virtual object, image is real. (iii) Image size = Object size.

(iv) The converging point of incident beam behaves as object.

(v) If incident beam on optical instrument (mirror, lens etc) is converging in nature, object is virtual.

(vi) If incident beam on the optical instrument is diverging in nature, the object is real.

(vii) The converging point of reflected or refracted beam from an optical instrument behaves a image.

(viii) If reflected beam or refracted beam from an optical instrument is converging in nature, image is real. Real Image P Virtual Object P n n

(ix) If reflected beam or refracted beam from an optical instrument is diverging in nature,

P P’

Real

Object Virtual_Object n n     image is virtual.

(x) For solving the problem, the reference frame is chosen in which optical instrument (mirror, lens, etc.) is in rest.

(xi) The formation of image and size of image is independent of size of mirror.

(xii) Visual region and intensity of image depend on size of mirror.

(xiii) If the plane mirror is rotated through an angle , the reflected ray and image is rotated through an angle 2 in the same sense.

(xiv) If mirror is cut into a number of pieces, then the focal length does not change.

(xv) The minimum height of mirror required to see the full image of a man of height h is h/2.

Image Rest Object (xvi) v Image Rest Object (xvii) v sin v sin v cos v cos  Image Rest Object (xviii) v vm 2 v - vm Image Object In rest (xix) vm 2 vm Image Object (xx) v vm 2 v + vm

(C) Number of images formed by combination of two plane mirrors : The images formed by

combination of two plane mirrors are lying on a circle whose centre is at the meeting points of mirrors. Also, object is lying on that circle.

Here,

 

 360

n

where  = angle between mirrors. (i) If

  360

is even number, the number of image is n–1.

(ii) If 

 360

is odd number and object is placed on bisector of angle between mirrors, then number of images is n–1.

(iii) If 

 360

is odd and object is not situated on bisector of angle between mirrors, then the number of images is euqal to n.

(D) Law of reflecteion in vector form :

Let eˆ₁ = unit v ecotr along incident ray.. Let eˆ₂ = unit v ector along reflected ray

n nˆ

1

ˆ ˆ₂

nˆ = unit vector along normal on point of incidence Then, eˆ₂ eˆ₁2



eˆ₁.nˆ



nˆ

(e) Spherical mirrors :

x x’ y’ y x x’ y’ y x x’ y’ y x x’ y’ y x x’ y’ y

(ii) The mirror formula is

    1 u 1 1 Also, R = 2 

These formulae are only aplicable for paraxial rays.

(iii) All distances are measured from optical centre. It means optical centre is taken as origin. (iv) The sign convention are only applicable in given values.

(v) The transverse magnification is u size object size image    

1. If object and image both are real,  is negative.

2. If object and image both are virtual,  is negative

3. If object is real but image is virtual;  is positive.

4. If object is virtual but image is real,  is positive.

D F d Sun  

5. Image of star; moon or distant object is formed

at focus of mirror.

If y = the ddistance of sun or moon from earth. D = diameter of moon or sun’s disc.

 = focal length of the mirror d = diameter of the image

 = the angle subtended by sun or moon’s disc Then tan =  =   d y D Here,  is in radian.

Laws of Refraction

1. (a)The incident ray, the refracted ray and normal on incidence point are coplanar.

(B) ₁sin₁₂sin₂ constant.

1  2  2  1 

(C) Snell’s law in vector form:

1  2  2 ˆ 1 ˆ nˆ

Let, eˆ₁ = unit v ector along incident ray

2

nˆ = unit vector along normal on incidence point. Then ₁



eˆ₁nˆ



₂



eˆ₂nˆ



.

Some important points :

(i) The value of absolute retractive index  _{is always greater or equal to one.}

(ii) The value of refractive index depends upon material of medium, colour of light and temperature of medium.

(iii) When temperature increases, refractive index decreases.

(iv) Optical path is defined as product of geometrical path and refractive index. i.e., optical path = _x

(v) For a given time, optical path remains constant. i.e., ₁x₁₂x₂   constant

 1dx_dt1 2dx_dt2  1c12c2  2 1 1 2 c c    i.e., c 1  

(vi) The frequency of light does not depend upon medium.

 c11, c22  1 2 1 2 2 1 c c           1

2. (a) When observer is in rarer medium and object is in denser medium: Then depth apparent depth real  

(B) When object is in air and observer is in

Air Observer Denser medium ( ) P’ Object Apparent depth P Real depth denser medium: position real position apparent  

(C) The shift of object due to slab is         t 1 1 x

(i) This formula is ony applicable when observer is in rarer medium.

(ii) The object shiftness does not depend upon the

P P’ Q Object shiftness = x t position of object.

(iii) Object shiftness takes place in the direction of incidence ray.

(D) The equivalent rerfractive index of a combination of a number of slabs for normal incidence

is i i i t t      Here,  = tt_{i 1} + t₂ + ... t₁ 1 2 t2         2 2 1 1 i i t t t

(e) The apparent depth due to a number of media is i i t   _. i t r d 

(f) The lateral shifting due to a slab is d = t sec r sin (i – r).

3. (a) Cricital angle : When a ray passes from denser medium ( )₂ to rarer medium ( ), then for 90° angle of refraction, the₁

c Rarer 1 Denser 2 90°

corresponding angle of incidence is critical angle. Mathematically, 2 1 C sin   

(B) (i) When angle of incidence is lesser than

critical angle, refraction takes place. the corresponding deviation is i i sin sin 1 2 1 _              _{for i = C} Rarer medium ( )1 i r c i _i i < C i = C Denser medium ( )2

(ii) When angle of incidence is greater than critical angle, total internal reflection takes place. the corresponding dev iation is

i 2     when i > C 4. The i graph is

(i) Critical angle depends upon colour of light, material of medium,

c i 

/2

and temperature of medium.

(ii) Critical angle does not depend upon angle of incidenct.

PRISM

(a) Deviation produced by prism is

_

_

_i

_

_i

_

_

_A

.

(B) r + r ’ = A

(C) For grazing incidence, i = 90° (D) For grazing emergence, i’ = 90°

(e) For not transmitting the ray from prism,  _{> cosec} 2 A A B C n n’ r’ r i _i’

(f) For limiting angle of prism, i = i’ = 90°, the limiting angle of prism = 2C where C is critical angle. If angle of prism exceeds the limiting values, then the rays are totally reflected.

(g) i graph for prism: (h) For minimum deviation,

(i) i = i’ and r = r’ (ii)

2 A sin 2 A sin m          i  m

In the case of minimum deviation, ray is passing through prism symmetrically. (i) For maximum deviation



_max



.

i = 90° or i’ = 90° (j) For thin prism, 



1



A

(k) Angular dispersion, D



__r



A (l) Angular deviation, _y 



_y 1



A (m) dispersive power = _               1 y r (n)           2 r y

(o) For dispersion without deviation, y 0

(p) For deviation without dispersion, D 0 _{x’ A x}

B

O C

1 2

Refractive surface formula,

r u 1 2 1 2 _ _    

Here,  = image distance, u = object distance, r = radius of curvature of spherical surface (a) For plane surface, r = 

(B) Transverse magnification, u size object size age Im m 2 1     

(C) Refractive surface formula is only applicable for paraxial ray.

LENS

1. Lens formula :     1 u 1 1

(a) Lens formula is only applicable for thin lens.

(B) r = 2  formula is not applicable for lens.

(C) m _objectimage _sizesize _u

(D) Magnification formula is only applicable when object is perpendicualr to optical axis.

(e) Lens formula and the magnification formula is only applicable when medium on both sides of lenses are same.

(f) _f(+ve) (i) f(-ve) (ii) f(-ve) (iii) f(+ve) (iv) f(-ve) (v) f(+ve) (vi)

(g) This lens formula is applicable for converging as well diverging lens. 1 1 2

Thin lens maker’s formula :

                       _{1 1 2} 1 2 r 1 r 1 1

2. (a) Thin lens formula is only applicable for paraxial ray.

(B) This formula is only applicable when medium on both sides of lens are same. (C) Intensity is proportional to square of aperture.

(D) When lens is placed in a medium whose refractive index is greater than that of lens. i.e.,

2 1

 . Then conv erging lens behaves as diverging lens and vice versa.

(e) When medium on both sides of lens are not same. Then both focal lengths are not same to each other.

(f) If a lens is cut along the diameter, focal length does not change.

(g) If lens is cut by a vertical, it converts into two lenses of different

+ f f1 f2 focal lengths. i.e., 2 1 1 1 1     

(h) If a lens is made of a number of layers of different refractive index (shown in figure).

Then number of images of an object formed by the lens is

+ + + + + + 1 2 3 4 5 6

equal to number of different media.

(i) The minimum distance between real object and image in is 4  .

(j) The equivalent focal elngth of co-axial combination of two d<f1 d<f2

o1 o2 f1 f2 d lenses is given by 2 1 2 1 d 1 1 F 1       

(k) If a number of lenses are in contact, then       2 1 1 1 F 1

(l) (i) Power of thin lens, F

1 P 

(ii) Power of mirror is F 1 P

(m) If a lens is silvered at one surface, then the system behaves as an equivalent mirror, whose power P = 2P_L + P_m

Here, P_L = Power of lens = 

                   2 1 1 1 2 r 1 r 1

P_m = Power of silvered surface

m F 1   Here, 2 r

F_m  2 , where r₂ = radius of silvered surface.

F 1 P

ASSERTION & REASION

THE NEXT QUESTIONS REFER TO THE FOLLOWING INSTRUCTIONS

A statement of assertion (A) is given and a Corresponding statement of reason (R) is giv en just below it of the statements, mark the correct answer as –

(A) If both A and R are true and R is the correct explanation of A.

(B) If both A and R are true but R is not the correct explanation of A.

(C) If A is true but R is false.

(D) If both A and R are false.

(E) If A is false but R is true.

1. Assertion (A) : A single ray can’t be isolated from a source however small it may be.

Reason (R) : The concept of single ray is hypothetical.

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

2. Assertion (A) : Virtual images can be photographed.

Reason (R) : Rays from virtual images are diverging.

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

3. Assertion (A) : Virtual object can’t be seen by human eye.

Reason (R) : Virtual object is formed by converging rays.

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

4. Assertion (A) : A Convex mirror is used as rear v iew mirror.

Reason (R) : The Convex mirror always forms virtual, erect and diminished image.

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

5. Assertion (A) : The behavior of any lens depends on surrounding medium.

Reason (R) : A lens can be looked upon as a collection of small prism with varying prism angle.

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

6. Assertion (A) : Human eye can see virtual object.

Reason (R) : Virtual object is formed by apparent intersection of incident rays.

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

7. Assertion (A) : Real image is formed by real intersection of reflected or refracted rays.

Reason (R) : Real image can’t be obtained on screen.

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

8. Assertion (A) : If a portion of lens or mirror is blocked or removed, then intensity of image reduces.

Reason (R) : As every portion of lens or mirror forms image, hence blocking or removing a portion will result in intensity reduction.

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

9. Assertion (A) : A rectangular glass slab produces no deviation and no dispersion.

Reason (R) : Dispersiv e power of glass is zero.

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

10. Assertion (A) : A double convex lens



 

1.5



has focal length 10 cm. When immersed in water

4

3

















, its focal length becomes 40 cm.

Reason (R) : 1 2

1

_{l m}

1

1

m

f

R

R















_



_





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

11. Assertion (A) : A convex lens of glass



 

1.5



behave as diverging lens when immersed in carbon disulphide of higher refractive index



 

1.65



.

Reason (R) : A diverging lens is thinner in the middle and thicker at the edges.

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

12. Assertion (A) : A biconvex lens of focal length 10 cm is split into two equal parts by a plane parallel to its principal axis. The focal length of each part will be 20 cm.

Reason (R) : The focal length depends on how many parts the convex lens has been split.

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

13. Assertion (A) : Radius of curvature of a convex mirror is 20 cm. If a real object is placed at 10 cm from pole of the mirror, image is formed at infinity.

Reason (R) : When object is placed at focus, its image is formed at infinity.

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

14. Assertion (A) : For a prism of refracting angle 60° and refractive index

₂

, minimum deviation is 30°.

Reason (R) : At minimum deviation, 1 2

30

2

A

r



r







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

15. Assertion (A) : Image formed by concave lens is not always virtual.

Reason (R) : Image formed by a lens if the image is formed in the direction of ray of light with

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

16. Assertion (A) : Minimum deviation for a given prism does not depend on the refractive index



of the prism.

Reason (R) : Deviation by a prism is given by

 



i

₁



i

₂



A



and does not have the term



.

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

Level # 1.

Objective Type Question

Multiple Choice Question with ONE correct answer :

1. Two plane mirrors M₁ and M₂ are inclined to each other at 70°. A ray incident on the mirror M₁ at an angle

 falls on M₂ and is then reflected parallel to M₁ for

(A)  = 45° (B)  = 50° (C)  = 55° (D)  = 60°

2. A light ray is incident on a horizontal plane mirror at an angle of 45°. At what angle should a second plane mirror be placed in order that the reflected ray finally be reflected horizontally from the second mirror, as shown in figure.

(A)  = 30° (B)  = 24°

(C)  = 22.5° (D)  = 67.5°

3. A plane mirror is placed in z plane facing towards negative x-axis. The mirror is moving parallel to y-axis with a speed of 5 cm/s. A point object P is moving infront of the mirror with a velocity (3 cm/s) iˆ + (4 cm/s)jˆ _{+ (5 cm/s) kˆ . Find the velocity of image with respect to mirror}

(A) (–3 cm/s) iˆ + (4 cm/s)jˆ _{+ (5 cm/s) kˆ (B) (3 cm/s) iˆ + (4 cm/s)}jˆ _{+ (5 cm/s) kˆ}

4. The size of the face of a dancer is 24 cm x 16 cm. Find the minimum size of a plane mirror required to see the face of dancer completely by

(i) one eyed dancer. (ii) two eyed dancer.

(Distance between the eyes is 4 cm.)

(A) (i) 12 x 8 cm2 _{(ii) 12 x 6 cm}2 (B) (i) 8 x 10 cm2 _{(ii) 12 x 2 cm}2 (C) (i) 10 x 12 cm2 _{(ii) 9 x 8 cm}2 (D) (i) 12 x 2 cm2 _{(ii) 6 x 13 cm}2

5. A bullet of mass m₂ is fired from a gun of mass m₁ with horizontal velocity v. A plane mirror is fixed at gun facing towards bullet. The velocity of the image of bullet formed by the plane mirror with respect to bullet is (A) _        1 2 m m 1 _{(B) }        1 2 1 m m m (C)







 1 2 1 m m m 2 (D) none of these

6. In the given figure, the angle of reflection is

(A) 30° (B) 60°

(C) 45° (D) none of these.

7. Two plane mirrors A and B are aligned parallel to each other, as shown in figure. A light ray is incident at an angle of 30° at a point just inside one

end of A. The plane of incidence coincides with the plane of figure. The 0.2 m

A B 30° m 3 2

maximum number of times the ray undergoes reflections (excluding the first one) before it emerges out is

(A) 28 (B) 30 (C) 32 (D) 34

8. A point source of light B is placed at a distance L in front of the centre of a mirror of width d hung vertically on a wall as shown. A man walks in front of the mirror along a line parallel to the mirror at a distance 2L from it as shown.

d B

L 2 L

The greatest distance over which he can see the image of the light source in the mirror is

(A) ½ d (B) d (C) 2d (D) 3d

9. A plane mirror having a mass m is tied to the free end of a massless spring of spring constant k. The other end of the spring is attached to a wall. The spring with the mirror held vertically to the floor can slide along it smoothly. When the spring is at its natural length, the mirror

Wall k

is found to be moving at a speed of v cm/s. The separation between the images of a man standing before the mirror, when the mirror is in its extreme positions

(A) k m v (B) k m 2 v (C) k m v 2 (D) k m v 4

10. Two spherical mirrors M₁ and M₂, one convex and other concave having same radius of curvature R are arranged coaxially at a distance 2R (consider their pole separation to be 2R). A bead of radius a is placed at the pole of the convex mirror a shown. The

M₁ M₂

ratio of the size of the first three images of the bead is

(A) 1 : 2 : 3 (B) 1 : 3 1 : 2 1 (C) 41 1 : 11 1 : 3 1 (D) 3 : 11 : 41

11. An object is placed in front of a convex mirror at a distance of 50 cm. A plane mirror is introduced

covering the lower half of the convex mirror. If the distance between the object and the plane mirror is 30 cm, there is no parallax between the images formed by the two mirrors. The radius of curvature of the convex mirror (in cm) is

12. A rectangular glass slab ABCD of refractive index n₁, is immersed in water of refractive index n₂ (n₁ > n₂). A ray of light is incident at the surface AB of the slab as shown. The maximum value of the angle of incidence _max, such that the ray comes out only from the other surface CD is given by

(A)                             1 2 1 2 1 1 n n sin cos n n sin _(B)                             2 1 1 1 n 1 sin cos n sin (C) _        2 1 1 n n sin _{(D) }        1 2 1 n n sin

13. Two thin slabs of refractive indices 

1 and 2 are placed parallel to

each other in the x-z plane. If the direction of propagation of a ray in the two media are along the vectors _{r aiˆ bjˆ}

1  and r2 ciˆdjˆ x y 2 1 then we have (A) ₁a₂b (B) ₂1 _{2 2}2 ₂ d c c b a a      (C)  1 (a 2 _{+ b}2_{) = } 2 (c 2 _{+ d}2_{) (D) none of these}

14. A man stands on a glass slab of height  and inside an elevator accelerated upwards with ‘a’. The bottom of the slab appears to have shifted with respect to the man by a distance (if the R. I. of the glass is 

g)

(A) less then  g (B) greater than g (C) equal to g (D) can’t be said.

15. A ray of light travels from a medium of refractive index  into air. If the angle of incidence at the plane surface of separation is  and the corresponding angle of deviation is D, the variation D with  is shown correctly by the figure.

C C C D D D D D1 D1 D1 _D 2 D2 D2 (0, 0) (0, 0) (0, 0) (0, 0)  /2  _ /2 _{ /2} (A) (B) (C) (D)

16. An observer can see through a pin hole at the top end of a thin rod of height

h placed as shown in the figure. Beaker height is 3h and its radius is h. When the beaker is filled with a liquid up to a height 2h, he can see the

h

2 h 3 h

Eye

lower end of the rod. Then refractive index of the liquid is

(A) 2 3 (B) 2 3 (C) 2 5 (D) 2 5 . (Assume that the distance between rod and the wall is negligible).

17. A glass sphere of radius 5 x 10–2 _{m has a small bubble 2 x 10}–2 _{m from its centre. Bubble is viewed along}

the diameter of the sphere, from the side on which it lies. If refractive index of glass is 1.5 then how far from the surface will the bubble appear?

18. A ray of light travelling in a transparent medium falls on a surface separating the medium from air at an

angle of incident 45°. The ray undergoes total internal reflection. If  is the refractive index of the medium with respect to air, select the possible value(s) of  _{from the following :}

(A) 1.3 (B) 1.4 (C) 1.5 (D) 1.7

19. A tank contains a transparent liquid of refractiv e index n the bottom of which

is made of a mirror as shown. An object O lies at a height d above the mirror. A person P vertically above the object sees O and its image in the mirror and

d O

P

finds the apparent separation to be

(A) 2nd (B) 1 n d 2  (C) n d 2 (D)



1 n



n d 

20. A fish looks up at the surface of a perfectly smooth lake. The surface appears dark except a circular

area directly above it. The plane angle  that this illuminated region subtends is

(A) 48.6° (B) 24.3° (C) 97.2° (D) 12.15°

21. A ray of light enters an anisotropic medium from vacuum at grazing incidence. If  is the angle made by the reflected ray inside the medium with the interface and n() is the refractive index of the medium then,

(A) n() sin = 1 (B) n() cos = 1 (C) 1 sin ) ( n    (D) 1 cos ) ( n   

22. The slab of a material of refractive index 2 shown in figure has

a curved surface. APB of radius of curvature 10 cm and a plane surface CD. On the left of APB is air and on the right of CD is water with refractive indices as given in figure. An object O is placed at a distance of 15 cm from pole P as shown. The

distance of the final image of O from P, as viewed from the left is

(A) 20 cm (B) 30 cm (C) 40 cm (D) 50 cm

23. An object is placed at a distance of 12 cm from a convex lens on its principal axis and a virtual image of

certain size is formed. On moving the object 8 cm away from the lens, a real image of the same size as that of virtual image is formed. The focal length of the lens in cm is

(A) 15 (B) 16 (C) 17 (D) 18

24. 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 the 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 the point O and PO = OQ. The distance PO is equal to

(A) 5 R (B) 3 R (C) 2 R (D) 1.5 R

25. A lens of focal length  is placed in between an object and screen fixed at a distance D. The lens forms

two real images of object on the screen for two of its different positions, a distance x apart. The two real images have magnifications m₁ and m₂ respectively (m₁ > m₂).

(A) 2 1 m m x    _{(B) m} 1 m2 = 1 (C) _4D x D2 2 

26. A liquid of refractive index 1.33 is placed between two identical

plano-convex lenses, with refractive index 1.50. Two possible

P Q

arrangement P and Q are shown. The system is

(A) divergent in P, convergent in Q. (B) convergent in P, divergent in Q. (C) convergent in both

(D) divergent in both.

27. A lens of refractive index  _{is put in a liquid of refractive index  . If the focal length of the lens in air is}  , its focal length in liquid will be

(A)





        1 (B)



_

_



1        (C)

_





_

       1 (D)

_

_

     

28. A convergent lens is placed inside a cell filled with a liquid. The lens has a focal length +20 cm when in

air and its material has a refractive index 1.50. If the liquid has a refractive index 1.60, the focal length of the system

(A) –160 cm (B) – 24 cm (D) –80 cm (D) + 80 cm

29. A double convex lens, made of glass of refractive index 1.5, has focal length 6 cm. The radius of curvature

of one surface is double than that of other surface. The small radius of curvature has value

(A) 4.5 cm (B) 6 cm (C) 4 cm (D) 9 cm

30. If the distance between a projector and screen is increased by 1%, then illumination on the screen

decreases by

(A) 1 % (B) 2 % (C) 3 % (D) 4 %

31. A lens forms a sharp image of a real object on a screen. On inserting a parallel slide between the lens

and the screen with its thickness along the principal axis of the lens it is found necessary to shift the screen parallel to itself ‘d’ away from the lens for getting image sharply focused on it. If the refractive index of the glass relative to air is , the thickness of slab is

(A)  d (B) d (C) 1 d    (D)





   1 d

32. A thin convex lens in used to form a real image of a bright point object. The

apeture of the lens is small. A graph, shown is obtained by plotting a suitable

O

X Y

-1 

parameter Y against another suitable parameter x. If  = the focal length of the lens

u = object distance v = image distance

and Real Positive Convention is used then

(A) (uV)  x; (u + V)  y (B) (u + V)  x; (uV)  y

(C) u  x; v u  y (D) u 1  x; v 1  y

33. Which of the following best represents object distance u vs image distance v graph for a convex lens. (A) y  (B) y  (C) y  (D) y 

34. Three thin prisms are combined as shown in figure. The refractive indices of the crown glass for red,

yellow and violet rays are 

r, y and v respectively and those for the flint glass are ’r, ’y and ’v

respectively. The ratio A’/A for which there is no net angular dispersion.

(A)





1 1 2 y y     (B) y y y y 2 _       (C)







y



y y y 1 1         (D) y y y y. 2       

35. A point object is placed at distance of 0.3 m from a convex lens of focal length

0.2 m cut into two equal halves, each of which is displaced by 0.0005 m, as shown in figure. If C₁ and C₂ be their optical centres then,

(A) an image is formed at a distance of 0.6 m from C₁ or C₂ along principal axis.

(B) two images are formed, one at a distance of 0.6 m and other at a distance O C1 C2

of 1.2 m from C₁ or C₂ along principal axis.

(C) an image is formed at a distance of 0.12 m from C₁ or C₂ along principal axis.

(D) two images are formed at a distance of 0.6 m from C₁ or C₂ along principal axis at a separation of 0.003 m.

36. A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3). A light beam incident normally on the face AB is totally reflected to reach on the face BC if (1983)

A B  (A)

sin

8

9





(B)

2

sin

8

3





9

(C)

2

sin

3





37. A ray of light from a denser medium strike a rarer medium at an angle of incidence i (see Figure). The reflected and refracted rays make an angle of 90° with each other. The angles of reflection and refraction are r and r’ The critical angle is

i r

r'

38. Two coherent monochromatic light beams of intensities

_

and 4

_

are superposed. The maximum and minimum possible intensities in the resulting beam are

(A) 5

_

and

_

(B) 5

_

and 3

_

(C) 9

_

and

_

(D) 9

_

and 3

_

39. An isosceles prism of angle 120° has a refractive index 1.44. The parallel monochromatic rays enter the prism parallel to each other in air as shown. The rays emerge from the opposite faces

120°

(A) are parallel to each other (B) are diverging

(C) make an angle 2 [sin–1 _{(0.72) – 30°] with each other} (D) make an angle 2 sin–1 _{(0.72) with each other}

40. A diminished image of an object is to be obtained on a screen 1.0 m from it. This can be achieved by appropriately placing

(A) a concave mirror of suitable focal length (B) a convex mirror of suitable focal length (C) a convex lens of focal length less than 0.25 m (D) a concave lens of suitable focal length 41. A concave lens of glass, refractive index 1.5 has both surfaces of same radius of curvature R. On

immersion in a medium of refractiv e index 1.75, it will behave as a

(A) convergent lens of focal length 3.5 R (B) convergent lens of focal length 3.0 R (C) divergent lens of focal length 3.5 R (D) divergent lens of focal length 3.0 R 42. A hollow double concave lens is made of very thin transparent material. It can be filled with air or either

of two liquids L₁ and L₂ having refractive indices



₁ and



₂ respectively





₂





₁



1



. the lens will diverge a parallel beam of light if it is filled with

(A) air and placed in air (B) air and immersed in L₁ (C) L₁ and immersed in L₂ (D) L₂ and immersed in L₁

43. A diverging beam of light from a point source Is having divergence angle



, falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is t and the refractive index n, then the divergence angle of the emergent beam is

(A) zero (B)



(C)

sin

1

1

n















(D) 1

1

2sin

n



 

 

 

44. A ray of light passes through four transparent media with refractive indices



₁,



₂,



₃ and



₄ as shown in the figure. the surfaces of all media are parallel. If the emergent ray CD is parallel to the incident ray AB, we must have

45. A given ray of light suffers minimum deviation in an equilateral prism p, Additional prism Q and R of identical shape and of the same material as P are now added as shown in the figure. The ray will now suffer

P Q R

(A) greater deviation (B) no deviation

(C) same deviation as before (D) total internal reflection

46. Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of the surfaces of the lenses are as given in the diagrams.

(A) R1 R2 (B) R (C) R R (D) R

47. Two plane mirrors A and B are aligned parallel to each other, as shown in the figure A light ray is incident at an angle 30° at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is

(A) 28 (B) 30 (C) 32 (D) 34

48. The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 2 0 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image.

(A) 1.25 cm (B) 2.5 cm (C) 1.05 cm (D) 2 cm

49. A ray of light is incident at the glass-water interface at an angle i, it emerges finally parallel to the surface of water, then the v alue of



g would be

(A)



4 3 sin i



(B)

1 sin i

(C)

4 3

(D) 1

50. A beam of white light is incident on glass air interface from glass to air such that green light just suffers total internal reflection. The colors of the light which will come out to air are

(A) Violet, Indigo, Blue (B) All colors except green (C) Yellow, Orange, Red (D) White light

51. An equilateral prism is placed on a horizontal surface. A ray pQ is incident onto it. For minimum deviation

P Q

R S

(A) PQ is horizontal (B) QR is horizontal

(C) RS is horizontal (D) Any one will be horizontal

52. A source emits sound of frequency 600 Hz inside water. The frequency heard in air will be equal to (velocity of sound in water = 1500 m/s, velocity of sound in air = 300 m/s)

(A) 3000 Hz (B) 120 Hz (C) 600 Hz (D) 6000 Hz

53. A point object is placed at the centre of a glass sphere of radius 6 cm and refractive index 1.5. The distance of virtual image from the surface is

(A) 6 cm (B) 4 cm (C) 12 cm (D) 9 cm

54. A convex lens is in contact with concave lens. the magnitude of the ratio of their focal length is

2 3

. Their equivalent focal length is 30 cm. What are their individual focal lengths?

(A) –15, 10 (B) –10, 15 (C) 75, 50 (D) –75, 50

55. A container is filled with water



 

1.33



upto a height of 33.25 cm. A concave mirror is placed 15 cm above the water level and the image of an object placed at the bottom is formed 25 cm below the water level. Focal length of the mirror is

(A) 15 cm (B) 20 cm (C) –18, 31 cm (D) 10 cm

Multiple Choice Question with ONE or MORE THAN ONE correct answer:

56. A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm. The power of the combination is

(A) –1.5 dioptres (B) –6.5 dioptres (C) +6.5 diopres (D) +6.67 dioptres 57. A converging lens is used to form an image on a screen. When the upper half of the lens is covered by

an opaque screen

(A) half the image will disappear (B) complete image will be formed (C) intensity of the image will increase (D) intensity of the image will decrease.

58. A short linear object of length b lies along the axis of a concave mirror of focal length f at a distance u from the pole of the mirror. The size of the image is approximately equal to

(A) 1 2

u

f

b

f















(B) 1 2

f

b

u

f















(C)

u

f

b

f















(D) 2

f

b

u

f















59. A beam of light consisting of red, green and blue colours is incident on a right angled prism, figure. The refractive indices of the material of the prism for the above red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively. The prism will

45°

(A) separate part of the red colour from the green and blue colours (B) separate part of the blue colour from the red and green colours (C) separate all the three colours from one another.

(D) not separate even partially any colour from the other two colours.

60. A thin prism P₁ with angle 4° and made from glass of refractive index 1.54 is combined with another thin prism P₂ made from glass of refractive index 1.72 to produce dispersion without dev iation. The angle of the prism P₂ is

(A) 5.33° (B) 4° (C) 3° (D) 2.6°

61. Two thin convex lenses of focal lengths f₁ and f₂ are separated by a horizontal distance d (where

1 2

d



f



d



f

) and their centres are displaced by a vertical separation

_

as shown in Figure.

Taking the origin of coordinates O, at the center of the first lens the x and y coordinates of the focal point of this lens system, for a parallel beam of rays coming from the left, are given by:

(A) 1 2 1 2

,

f f

x

y

f

f



 



(B)





1 2 1 2 1 2

,

f

f

d

x

y

f

f

d

f

f















(C)









1 2 1 1 1 2 1 2

,

f f

d f

d

f

d

x

y

f

f

d

f

f

d





















(D)





1 2 1 1 2

,

0

f f

d f

d

x

y

f

f

d













62. Which of the following form(s) a v irtual and erect image for all positions of the object?

(A) Convex lens (B) Concav e lens (C) Convex mirror (D) Concave mirror. 63. A ray of light travelling in a transparent medium falls on a surface separating the medium from air at an

angle of incidence of 45°. The ray just undergoes total internal reflection. If n is the refractive index of the medium with respect to air, select the possible v alue(s) of n from the following:

(A) 1.3 (B) 1.4 (C) 1.5 (D) 1.6

64. A concave mirror is placed on a horizontal table, with its axis directed vertically upwards. Let O be the pole of the mirror and C its centre of curvature. A point object is placed at C. It has a real image, also located at C. 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

Fill in the blanks:

1. A light wave of frequency 5 x 1014 _{Hz enters a medium of refractive index 1.5, In the medium the}

velocity of the light wave is ... and its wavelength is ... (2 Marks) 2. 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 d is equal to ... cm.

3. A monochromatic beam of light of wavelength 6000Å in vacuum enters a medium of refractive index 1.5. In the medium its wavelength is ..., its frequency is ... (1985)

4. In young’s double-slit experiment, the two slits act as coherent sources of equal amplitude ‘A’ and of wavelength ‘

_

’. In another experiment with the same set-up the two slits are sources of equal amplitude ‘A’ and wav elength ‘

_

’, but are incoherent. The ratio of the intensity of light at the midpoint of the screen in the first case to that in the second case is ... (1986)

5. A thin lens of refractive index 1.5 has 7a focal length of 15 cm in air. when the lens is placed in a

medium of refractive index

4

3

, its focal length will become ... cm. (1987)

6. A point source emits sound equally in all directions in a non-absorbing medium. Two points P and Q are at a distance of 9 meters and 25 meters respectively from the source. The ratio of amplitudes of the waves at P and Q is ... (1989)

7. A slab of a material of refractive index 2 shown in Figure, has a curved surface APB of radius of curvature 10 cm and a plane surface CD. On the left of APB is air and on the right of CD is water with refractive indices as given in the figure.

A B C D P C O n =1.01 n =2.02 20 cm 15 cm 3 4 3 n =

An object O is placed at a distance of 15 cm from the pole P as shown. The distance of the final image

of O from P, as viewed from the left is ... (1991)

8. A thin rod of length

3

f

is placed along the optic axis of a concave mirror of focal length f such that itss image which is real elongated, just touches the rod. The magnification is ... (1991)

9. A ray of light undergoes deviation of 30° when incident on an equilateral prism of refractive index

₂

. The angle made by the ray inside the prism with the base of the prism is ... (1992)

10. A light of wavelength 6000Å in air, enters a medium with refractive index 1.5. Inside the medium its

11. Two thin lenses, when in contact, produce a combination of power +10 diopters. When they are 0.25 m apart, the power reduces to +6 diopters. The focal length of the lenses are ... m and .... m.

(1997)

12. A ray of light is incident normally on one of the faces of a prism of apex angle 30° and refractive index

2

. The angle of deviation of the ray is ... degrees. (1997)

True / False :

13. The intensity of light at a distance ‘r’ from the axis of a long cylindrical source is inversely proportional

to ‘r’. (1981)

14. A convex lens of focal length 1 meter and a concave lens of focal length 0.25 meter are kept 0.75 meter apart. A parallel beam of light first passes through the convex lens, then through the concave

lens and moves to a focus 0.5 m away from the concave lens. (1983)

15. A beam of white light passing through a hollow prism give no spectrum. (1983) 16. A parallel beam of white light fall on a combination of a concave and a convex lens, both of the same

material. Their focal lengths are 15 cm and 30 cm respectively for the mean wavelength in white light. On the other side of the lens system, one sees coloured patterns with v iolet colour at the outer edge.

(1988)

Table Match

17. Match List I and List II and select the correct answer using the codes given below the lists:

The arrangement shows different lenses made of substance of refractive index 1.5 and kept in air. R₁ = 30 cm, R₂ = 60 cm. Match the focal lengths

Table I Table II I. R1 R2 A. –120 cm II. R1 R2 B. +40 cm III. R1 R2 C. –40 cm IV. R1 R2 _{D. +120 cm}

(A) I-A, II-B, III-D, IV-C (B) I-C, II-A, III-B, IV-D (C) I-D, II-C, III-A, IV-B (D) I-B, II-D, III-C, IV-A

18.

Table I Table II

I. An object is placed at focus before A. Magnification is –

_

a convex mirror

II. An object is placed at the centre of B. Magnification is +0.5

curvature before a concav e mirror

III. An object is placed at focus before C. Magnification is +1

a concave mirror.

IV. An object is placed at centre of curvature D. Magnification is – 1 before a convex mirror.

(A) I-B, II-D, III-A, IV-E (B) I-A, II-D, III-C, IV-B (C) I-C, II-B, III-A, IV-E (D) I-B, II-E, III-D, IV-C

19. Match the followings:

Table I Table II

A. Magnification m = +1 (i) Convex mirror

B. Magnification

2

3

m  

(ii) Plane mirror

C. Magnification

3

2

m  

(iii) Concave mirror

(A) A



(ii) B



(iii) C



(i) (B) A



(i) B



(ii) C



(iii)

(C) A



(ii) B



(i) C



(iii) (D) A



(iii) B



(ii) C



(i)

20. For a concave mirror of focal length 20 cm, match the followings:

Table I Table II

Objective distance Nature of image

A. 10 cm (i) Magnified, inverted and real

B. 30 cm (ii) Equal size, inv erted and real

C. 40 cm (iii) Smaller, inverted and real

D. 50 cm (iv) Magnified, erect and virtual

(A) A



II, B



I, C



III, D



IV (B) A



IV, B



I, C



II, D



III

(C) A



I, B



IV, C



III, D



II (D) A



IV, B



I, C



III, D



II.

PASSAGE TYPE QUESTIONS

THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE

The ciliary muscles of eye control the curvature of the lens in the eye and hence can alter the effective focal length of the system. When the muscles are fully relaxed, the focal length is maximum. When the muscles are strained the curvature of lens increases (that means radius of curvature decreases) and focal length decreases. For a clear vision, the image must be on retina. The image distance is therefore fixed for clear vision and it equals the distance of retina from eye-lens. It is about 2.5 cm for a grown-up person.

A person can theoretically have clear vision of objects situated at any large distance from the eye. The smallest distance at which a person can ciliary muscles are most strained in this position. For an average grown-up person, minimum distance of object should be around 25 cm.

A person suffering for eye defects uses spectacles (eye glass). The function of lens of spectacles is to form the image of the objects within the range in which person can see clearly. The image of the spectacle lens becomes object for eye-lens and whose image is formed on retina. The number of spectacle lens used for the remedy of eye defect is decided by the power of the lens required and the number of spectacle-lens equal to the numerical v alue of the power of lens with sign. For example, power of lens required is +3 D (converging lens of focal length

100

3

cm), then number of lens will be +3.

For all the calculations required you can use the lens formula and lens maker’s formula. Assume that the eye lens is equiconvex lens. Neglect the distance between eye lens and the spectacle lens.

1. Minimum focal length of eye-lens of a normal person is

(A) 25 cm (B) 2.5 cm (C)

25

9

cm

(D)

25

11

cm

2. Maximum focal-length of eye lens of normal person is

(A) 25 cm (B) 2.5 cm (C)

25

9

cm

(D)

25

11

cm

3. A near-sighted man can clearly see object only upto a distance of 100 cm and not beyond this. The number of the spectacles lens necessary for the remedy of this defect will be

(A) + 1 (B) – 1 (C) + 3 (D) – 3

4. A far-sighted man cannot see object only upto a distance of 100 cm from his eyes. The number of the spectacles lens that will make his range of clear vision equal to an average grown up person is

(A) + 1 (B) – 1 (C) + 3 (D) – 3

5. A person who can see objects clearly from distance 10 cm to

_

, then we can say that the person is

(A) normal sighted person (B) near-sighted person

(C) far-sighted person (D) a person with exceptional eyes having no eye defect. THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE

Spherical aberration in spherical mirrors is a defect which is due to dependence of focal length

'

f

'

on angle of incidence

_{' '}

_

as shown in figure. is given by

sec

2

R

f



R





F C Pole (P) Principal axis f  

where R is radius of curvature of mirror and

_

is the angle of incidence. The rays which are closed to principal axis are called paraxial rays and the rays far away from principal axis are called marginal

rays. As a result of above dependence different rays are brought to focus at different points and the

6. If

f

p and

f

m represent the focal length of paraxial and marginal rays respectively, then correct relationship

is:

(A)

f

_p



f

_m (B)

f

_p



f

_m (C)

f

_p



f

_m (D) None

7. If angle of incidence is 60°, then focal length of this rays is:

(A) R (B)

2

R

(C) 2R (D) 0

8. The total deviation suffered by the ray falling on mirror at an angle of incidence equal to 60° is:

(A) 180° (B) 90° (C) Can’t be determined (D) None

9. For paraxial rays, focal length approximately is:

(A) R (B)

2

R

(C) 2R (D) None

10. Which of the following statements are correct regarding spherical aberration:

(A) It can be completely eliminated

(B) it can’t be completely eliminated but is can’t be minimised by allowing either paraxial or marginal

rays to hit the mirror

(C) It is reduced by taking large aperture mirrors (D) None

THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE

Rainbow is formed during rainy season due to refraction and total internal reflection of rays falling on suspended water droplets. When rays of the sun fall on rain drops, the rain drops disperse the light and deviate the different colours by refraction and total internal reflection to the eye of the observer. A person observing the drops will see different colours of the spectrum at different angles. The rainbow which results from single total internal reflection is called primary rainbow and secondary rainbow is formed due to two total internal reflections suffered by rays falling on water drops.

A B C D V R R V Re d Red vio let violet Rays from sun Secondary rainbow Primary rainbow

Figure shows formation of rainbow due to four drops A, B, C and D. The light surffers only one total linternal reflection in drops C and D forming primary rainbow. Secondary rainbow is formed by drops A and B where light suffers two total linternal reflections.

11. Rainbow is an arc of:

(A) Circle (B) Ellipse

(C) Parabola (D) Can’t be determined 12. The visibility of the rainbow is due to:

(A) All rays (B) Rays undergoing maximum deviation (C) Rays undergoing minimum deviation (D) None

13. In primary rainbow, the colour of outer edge is:

(A) Blue (B) Violet (C) Red (D) None 14. In secondary rainbow, the colour of inner edge is:

(A) Red (B) Violet (C) Indigo (D) None

15. The necessary condition for the observer to see rainbow is:

(A) Sun, observer’s eye and the centre of the rainbow arc lie on the same line (B) Sun, observer’s eye and the centre of the rainbow arc lie on the different line

(C) From any position provided sun is at the back of the observer (D) None THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE

The laws governing the behavior of the rays namely rectilinear propagation, laws of reflection and refraction can be summarised in one fundamental also known as Fermat’s principle. According to this principle a ray of light travels from one point to another such that the time taken is at a stationary value (maximum or minimum). If c is the velocity of light in a vacuum, the velocity in a medium of refractive index n is

c

n

, hence time taken to travel a distance

l

is

nl

c

. If the light passes through a number of

media, the total time taken is

1

nl

c

 



 

 

and

1

n dl

c



. If refractive index varies continuously. Now, ,



nl

is the total optical path, so that Fermat’s principle states that the path of a ray is such that the optical path in at a stationary value. This principle is obviously in agreement with the fact that the ray are straight lines in a homogenous isotropic medium. It is found that it also agrees with the classical laws of reflection and refraction.

16. If refractive index of a slab v aries as

  

1 x

2 where x is measured from one end, then optical path length of a slab of thickness 1 m is:

(A)

4

3

m

(B)

3

4

m

(C) 1 m (D) None

17. The optical path length followed by ray from point A to B given that laws of reflection are obeyed as shown in figure is:

A B

P

(A) Maximum (B) Minimum (C) Constant (D) None

18. The optical path length followed by ray from point A to B given that laws of reflection are obeyed as shown in figure is

A B

19. The optical path length followed by ray from point A to B given that laws of refraction are obeyed as shown in figure is

A

B

(A) Maximum (B) Minimum (C) Constant (D) None

20. The optical path length followed by ray from point A to B given that laws of refraction are obeyed as shown in figure is

A and B are focii of ellipse

A B

(A) Maximum (B) Minimum (C) Constant (D) None THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE

One hard and stormy night you find yourself lost in the forest when you come upon a small hut. Entering it you see a crooked old woman in the corner hunched over a crystal ball. You are about to make a hasty exit when you hear the howl of wolv es outside. Taking another look at the gypsy you decide to take your chances with the wolves, but the door is jammed shut. Resigned to bad situation your approach her slowly, wondering just what is the focal length of that nifty crystal ball.

21. If the crystal ball is 20 cm in diameter with R.I. = 1.5, the gypsy lady is 1.2 m from the central of ball, where is the image of the gypsy in focus as you walk towards her?

(A) 6.9 cm from the crystal ball (B) 7.9 cm from the crystal ball (C) 8.9 cm from the crystal ball (D) None

22. The image of old lady is:

(A) real, inverted an enlarged (B) erect, virtual and small (C) erect, virtual and magnified (D) real, inverted and diminished

23. The old lady moves the crystal ball closer to her wrinkled old face. At some point you can no longer get an image of her. At what object distance will there be no change of the gypsy formed?

(A) 10 cm (B) 5 cm (C) 15 cm (D) None

THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE

The table below contains some physical properties of common optical materials. The refractive index of a material is a measure of the amount by which light is bent upon entering the material. The transmittance range is the range of wavelengths over which the material is transparent.

Physical Properties of Optical Materials

Material

Refractive

index for light

of 0.589 m

Transmittance

range (m)

Useful range

for prisms

(m)

Chemical

resistance

Lithium

fluoride

1.39

0.12-6

2.7-5.5

Poor

Calcium

fluoride

1.43

0.12-12

5-9.4

Good

Sodium

chloride

1.54

0.3-17

8—16

Poor

Quartz

1.54

0.20-3.3

0.20-2.7

Excellent

Potassium

bromide

1.56

0.3-29

15—28

Poor

Flint glass*

1.66

0.35—2.2

0.35-2

Excellent

Cesium iodide

1.79

0.3—7.0

15-55

Poor

*Flint glass is lead oxide doped quartz.

24. According to the table, which material(s) will transmit light at

25 m



–

(A) Potassium bromide only (B) Potassium bromide and cesium iodide (C) Lithium fluoride and cesium iodide (D) Lithium fluoride and flint glass

25. A scientist hypothesizes that any material with poor chemical resistance would have a transmittance range wider than 10



m

. The properties of which of the following materials contradicts this hypothesis–

(A) Lithium fluoride (B) Flint glass

(C) Cesium iodide (D) Quartz

26. When light travels from one medium to another, total internal reflection can occur if the first medium has a higher refractive index than the second. Total internal reflection could occur if light were travelling from–

(A) Lithium fluoride of flint glass

(B) potassium bromide to cesium iodide (C) quartz to potassium bromide

(D) flint glass to calcium fluoride

27. Based on the information in the table, how is the transmittance range related to the useful prism range–

(A) The transmittance range is always narrower than the useful prism range (B) The transmittance range is narrower than or equal tot he useful prism range (C) The tranmittance range increases as the useful prism range decreases

(D) The tranmittance range is wider than and includes within it the useful prism range 28. The addition of lead oxide to pure quartz has the effect of–

(A) decreasing the transmittance range and the refractive index

(B) decreasing the transmittance range and increasing the refractive index (C) increasing the transmittance range and the useful prism range

(D) increasing the transmittance range and decreasing the useful prism range. THE NEXT QUESTIONS REFER TO THE FOLLOWING PASSAGE

A periscope viewing system is to be used to observe the behavior of primates in a large environmentally controlled room on the upper floor of a large research facility. The periscope, like those used on

submarines, is essentially a large, folded-path, low power telescope (using prisms to fold the light path). A sketch of the preliminary design appears below. Like all Newtonian telescopes, it uses a relatively long focal length objective lens to form a real image in front of the eyepiece lens (of shorter focal length). The observer looks through the eyepiece lens to see the final image, in the same manner that one would use a magnifying glass.

The distance between the lenses is approximately equal to the sum of their focal lengths. The eyepiece, in this design, can be moved forward or back in order to focus on the primates as they move closer to or further away from the objective lens.

29. The total tube length of the three sections is to be 4 m. The objective lens available has a focal length of 3 m. What should the focal length of the eyepiece lens be?

(A) 0.75 m (B) 1 m (C) 1.33 m (D) 7 m

30. A visitor seeing the sketch points out an important flaw that will require a design change. what is the flaw?

(A) The focal length of the eyepiece lens is too short. (B) The images of the primates will be inverted (C) The objective lens should be a div erging lens. (D) The prisms cannot be used in this way.

31. A visitor seeing the sketch points out an important flaw that will require a design change. What is the flaw?

(A) The focal length of the eyepiece lens is too short. (B) The images of the primates will be inverted (C) The objective lens should be a div erging lens. (D) The prisms cannot be used in this way.

32. What will be the approximate magnification of this periscope?

(A) 0.67x (B) 1x (C) 3x (D) 300x

33. The prisms (45–45–90° prisms) turn the light path through 90° by “total internal reflection” from the inside hypotenuse faces of the prisms when the incident angle is 45° as in the sketch.

Can one use crown glass with an index of refraction of 1.52 for the prism?

(A) yes, because the critical angle for crown glass is 47° (B) yes, because the critical angle for crown glass is 41°. (C) No, because the critical angle for crown glass is exactly 47° (D) No, because the critical angle for crown glass is exactly 41°.

34. Describe the properties of the image that one sees with this preliminary design

(A) real, inverted, magnified (B) real, upright, magnified

(C) virtual, upright, same size as object. (D) virtual, inverted, magnified

35. The telescope is focused on a primate rather far away on the farside of the large habitat. As the primate moves rather closer to the telescope, what must the observer do to see the primate clearly?

(A) No change, the image remains clear. (B) Move the eyepiece away from the objective. (C) Move the eyepiece closer to the objective.