Optics Notes and MCQs

Notes 23 Pages

Joint Entrance Examination (Main)

Physics

Contributed by

Yash Kuruvilla

212
SUMMARY
 The path of the light propagation is called ray, but a bundald of such rays is called beam of light.
 The relation between focal length and radius of curvature is
2
R
f 
(for both the mirror) or R = 2f.
 In the case of plane mirror, R is infinite and therefore its focal length is also infinite.
 For mirrors, Gauss' equation is
,
R
2
f
1
v
1
u
1

where, u = object distance, v = image distance, f =
focal length, R = Radius of Curvature.
 Lateral magnification for mirrors is given by
u
v
h
'h
m 
, where,
'h
= height of image, h = height of
object.
 The ratio of the sine of the angle of incidence to the sine of the angle of refraction for the given two
media is constant, i.e.,
1
21
2
sin θ
= n
sin θ
= Constant.
where n
21
is known as the refraative index of medium–2 with respect to medium–1.
 For a compound slab of different transparent media general form of Snell's Law is written as:
1 1 2 2
n sinθ n sinθ
 Lateral shift x = t .
1
1
2
n
θ 1
n
 

 
 
 If two plane mirros M
1

and M
2

are inclined at angle
θ
, then no. of images form
360
n = -1
θ
 
 
 
 In concave mirror, when objects is between P and F, image formed is virtual, ereect and magnified.

m
is positive. However, when object lies beyond F, image formed is real and inverted.

m is negative.
 In convex mirror, image is always virtual and erect, whatever be the position of the object.
 Critical angle
1
1
C sin
n

 

 
 
where, n = refractive index medium.
As
rv
nn 

'C'.CC
rv
 increases with temperature.
Page 1
213
 Refraction from a spherical surface (for lens)
(1) For refrection from rarer to denser medium :
1 2 2 1
-n n n -n
+ =
u v R
(2) Form denser to rarer medium :
R
nn
u
n
v
n
1221



 Lens Maker's Formula is :
 
1 2
1 1 1
= n-1 -
f R R
 
 
 
For Convex lens : R
1

= +, R
2

= –, f = +
Convave lens : R
1

= –, R
2
= +, f = –
 Power of lens
1
f
P 
when f = 1m,

P = 1 diopter (D)
For Convex lens P = +,
Convave lens P = –
 If two lenses are in contact coaxilly,
(i)
2121
21
mmm)iii(PPP)ii(
f
1
f
1
f
1

 For Prism equation is given by
δ
= i + e – A or A+
δ
= i + e
At minimum angle of deviation,
δ
m
= 2i–A.
 
ei 
For thin prism
m
A(n 1)  
m
A δ
sin
2
n
A
sin
2

 
 
 

 
 
 
 Newton's formula f
2

= x
1

.x
2
 The relation between
δ
, A and n is :
δ
= A(n– 1)
Angular disperson,
v r v r
θ δ δ (n n )A   
Dispersive power
V r V r
δ -δ n n
ω = = ,
δ n 1


Where,
V r
n +n
n =
2
 (i) Resolving power of human eye = 1'
(ii) R.P. of Microscope =
2nsinθ
λ
(iii) R.P. of Telescope =
1.22.λ
D
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214
WAVE OPTICS
 Problem Solving Skills :
(1) Resultant intensity
2 2 2
I R b 2 bcosa a    
1 2 1 2
I I +I +2 I I cos 
If
021
III  ´ÜÜå
2
1 0 0 0 0
I = I + I + 2I cos 4 I cos

 
 
 

 
(2) Phase differance
 
2
x

  


Form
1 2 1 2
I = I +I +2 I I cos
When cos  = +1 


2
max 1 2 1 2 1 2
I I I 2 I I I I    
cos  = –1 
 
2
21min
III 
 
 
2
21
2
21
min
max
II
II
I
I




If the Sources are incoherent, I = I
1
+I
2

If W
1
and W
2

are widths of two Slis then ,
2
2
2
1
2
1
b
a
I
I
W
W


In the interfernce pattern
 
 
max
min
I
=
I
2
2
a+b
a - b
where a, b = Amplitude.

In young's double slit experiment
(a) Position of bright fringes
D
nλ
d
x  (where n = 0 for centeral fringe)
(b) Positiion of dark fringes x 


2n 1 λD
2d

(c) Width of each bright fringes = width of each darkfringes
λD
β
d
x 
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215
(d) when entire apparatus is immersed in a medium of refractve index n, fringe width becomes
'
'
λ D λD β
' β
d nd n n
x
x     
(e) Angular fringe width
d
λ
D
β

(f) fringe visibility is V = I
max
– I
min
/ I
max
+ I
min

A thickness t of a medium of refractive index n is equivalent to a length nt in vacuum or air. This is
called optical path length.

When a thin transperent plate of thickness t and refractive index n is placed in the path of one of the
interfering waves, fringe width remains unaffected but the entire patern shiffts by
   
D
1 t . 1 t
d
x n n

    


Law of Malus :

2
0
cosII

Brewster's law :
P
n = tan θ

the intensity of porlarised light :
2
I
I
0

where
0
I = intensity of unpolarsed light

Accoding to Doppler's effect for light waves
'
V
f f 1
C
 
 
 
 
where
'
f
= apparent frequency of light
f
= true frequency of light

A symbol of refractive index is also denoted by
µ
Page 4
216
MCQ Questions
(1). The velocity of light is maximum in a medium of________________.
(A) diamond (B) water (C) glass (D) vaccum
(2). A light of wavelength 320 nm enters in a medium of refractive index 1.6 from the air of refractive index
1.0 The new wavelength of light in the medium will be____________nm.
(A) 520 (B) 400 (C) 320 (D) 220
(3). "Bhautik" runs towards a plane mirror with a speed of 20 ms
–
1
, what is the speed of his image ?
(A) 45 ms
–
1
(B) 20 ms
–
1
(C) 15 ms
–
1
(D) 7.5 ms
–
1
(4). A ray of light is incident at an angle 30
0
on a mirror, The angle between normal and reflected ray
is___________.
(A)
15

(B)
30

(C)
45

(D)
60

(5). The no. of images formed between two parallel plane mirror are ______________.
(A)

(B) 0 (C) 180 (D) 360
(6). To get five images of a single object one shold have two plane mirrors at an angle of___________.
(A)
36

(B)
72

(C)
180

(D)
302

(7). If a glass rod is immersed in a liquid of the same refractive index, then it will______________.
(A) appear bent (B) appear longer (C) disappear (D) appear shorter
(8). For four different transperent medium
41 32 21
____________ .
n n n  
(A)
41
n
1
(B)
41
n
(C)
14
n
(D)
14
n
1
(9). A Plane mirror produces a magnification of_____________.
(A) 0 (B) +1 (C) –1 (D)

(10). A ray light passes through four transperent media
with refractive indices
4321
n,n,n,n as shown in
figure The surfaces of all media are parallel, if the
emergent ray DE is parallel of the incident ray AB
we must have_______________
E
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217
(A)
21
nn 
(B)
43
nn  (C)
41
nn 
(D)
32
nn 
(11). A convex lens forms a real image of an object for it s two different positons on a screen if hight of the
image in both cases be 16 cm and 4 cm then height of the object is__________cm.
(A) –4 (B) 4 (C) –8 (D) 8
(12). In shown figure two parallel rays incident on a
mirror they are reflected as paraller rays as shown
in the same figure what is the nature of the mirror ?
(A) plane mirror (B) concave
(C) convex (D) plano–concave
(13). The power of plane glass is__________.
(A)

(B) 0 (C) 2D (D) 4D
(14). A convex lens is made up of three diffrent materials as shown in figure, for
point object placed on its axis, the no. of imges formed are__________.
(A) 4 (B) 2
(C) 3 (D) 1
(15). Two thin lenses of focal lengths
1
f and
2
f are coaxially placed incontact with eachother then, the power
of combination is__________.
(A)
2
ff
21

(B)
2
1
f
f
(C)
21
21
ff
ff

(D)
21
21
ff
ff 
(16).

If thin prism of
5

gives a deviation of
2

then the refractive index of material of prism is_________.
(A) 1.4 (B) 1.5 (C) 1.6 (D) 1.0
(17). It is difficult to see through the fog because _________________
(A) light is seattered by the doplets in the fog.
(B) fog absorbs light.
(C) rafractive index of fog is infinity.
(D) light suffers totl internal reffection.
(18). what is the time taken in seconds to cross a glass plate of thikness 6 mm and
µ = 2.0
by light ?
(A)
11
108


(B)
11
104


(C)
11
102
(D)
11
1016


(19). Which of the following diagrams shows correctly the dispersion of white light by a prism ?
(A) (B) (C) (D)
Page 6
218
(20). Read the following quetions and choose if________________.
(A) both assertion and reason are true and the reason is correct explanation of the assertion.
(B) both assertion and reason are true but reason do not explain the assertion.
(C) Assertion is true but the reason are false.
(D) both assertion and reason are false.
(1) Assertion : Focal lengh of a lens for red colour is smaller than its focal length for violet colour
Reason : is becuse
r V
n n
(A) B (B) A (C) C (D) D
(21). In which of the following cases a man will not see image grater than himself.
(A) convex mirror (B) concave mirror (C) plane mirror (D) none of these
(22). A glass slab
 
n =1.5
of thikness 9 cm is placed over a written paper what is the Shift in the latters ?
(A) 6 cm (B) 3 cm (C) 2 cm (D) 0 cm
(23). A concave mirror of focal length 20 cm forms an virtual image having twice the linear dimensions of
the object, the position of the object will be ___________cm
(A) 7.5 (B) –10 (C) 10 (D) –7.5
(24). In experiment to find focal length of a concave mirror a graph is drawn between the magnitude of u and
v
.
The graph looks like___________.
(A) (B) (C) (D)
(25). A mark at the bottom of the liquid appears to rise by 0.2 m, If depth of the liquid is 2.0 m then refractive
index of the liquid is________________.
(A) 1.80 (B) 1.60 (C) 1.33 (D) 1.11
(26). A Sound wave travels from air to water. the angle of incidence is
1
α
and the angle of reflection is
2
α
If the snell's Law is valid then,___________________.
(A)
1 2
α

 (B)
21
α 
(C)
21
α 
(D)
21
α 
(27). 1.6 is a refractive index of plano-convex lens, then the redius of curvature of the curved sunface is 60
cm. The focal length of the lens is_______ cm
(A) 50 (B) 100 (C) –50 (D) –100
(28). One convex lens and one concave lens placed is contect with eachother. If the ratio of their power is
3
2
and focal length of the combination is 30 cm, then indivedual focal lengths are__________.
(A) 15 cm and –10 cm (C) 30 cm and –20 cm
Page 7
219
(B) –15 cm and 10 cm (D) –30 cm and –30 cm
(29). A thin prism of
3

, angle made from glass of refractive index 1.5 is combined with another thin prism
made from glass of refractive index 1.3 to produce dispersion without deveation. what is the angle of
Prism of second prism.
(A)

3
(B)

3
(C)

5
(D)

5
(30). If a ray of light is incident on a plane mirror at an angle of

30
then deviation produced by a plane
mirror is____________.
(A)
60

(B)
90

(C)
120

(D)
150

(31). The frequency of a light wave in a material is
14
4 10
z
H
and wavelensth is 5000

A

. The
refractive index of material will be____________ ( take
8 -1
3×10 m sc =
)
(A) 1.5 (B) 1.7 (C) 1.33 (D) None of thense
32. Mono chromatic light of wavelength 399 nm is incident from air on a water
 
n 1.33
Surface.
The wavelength of refracted light is ________________nm
(A) 300 (B) 600 (C) 333 (D) 443
33. If the refractive index of a material of an equilateral Prism is
3
, then angle of minimum deviation will
be____________.
(A)

50
(B)

60
(C)

39
(D)

49
34. If the critical angle for total internal reflection from a medium to vacuum is

30
then velocity of light
in the medium is _____________ms
–
1
( take c = 3.0

10
8
ms
–1

)
(A) 2.0

10
8
(B) 1.5

10
8
(C) 10
8
(D) 1.5

10
–
8
35. A ray of light passes from glass
 
n 1.5
to medium
 
n 1.60
The value of the critical angle of
glass is___________.
(A)







15
16
sin
1
(B)
15
16
sin
1
(C)







2
1
sin
1
(D)







16
15
sin
1
36. A double convex lens of focal length 6 cm is made of glass of refractive index 1.5, The radius of
curvature of one surface is double than that of the other surface. The value of small radius of curvature
is_________.
(A) 6 (B) 9 (C) 12 (D) 4.5
37. When a ray of light enters in a transperent medium of refractive index n, then it is observed that the
angle of refraction is half of the angle of incidence. The value of angle of incidence will be _________.
Page 8
220
(A)
-1
n
2cos
2
 
 
 
(B)
-1
n
cos
2
 
 
 
(C)
-1
n
2sin
2
 
 
 
(D)
-1
n
sin
2
 
 
 
38. A prsim of glass is shown in figure A, ray incident normally on
one face is totally reflected. If
θ
is

45
, the index of refraction
of glass is_____________.
(A) <
2
(B) >
2
(C) = 2 (D) None of these
39. A convex lens made up of a material of refractive index
1
n is
immersed in a medium of refractive index
2
n as shown in the
figure. The relation between n
1
and n
2
is___________.
(A)
1 2
n n
(B)
1 2
n n
(C)
1 2
n n
(D)
1 2
n n
40. Two plano–convex lenses of radius of curvature R and refractive index
n 1.5
will have equivalent
focal length equal to R, when they are placed__________.
(A) at distance R (C) at distance
4
R
(B) at distance
2
R
(D) in contact with each other
41. A double convex lens made of glass of refractive index 1.6 has radius of curvature 15 cm each. The focal
length of this lens when immersed in a fluid of refractive index 1.63 is____________.
(A) –40.75 (B) –407.5 (C) –125 (D) 12.5
42. One ray of light suffers minimum deviation in an equilateral
prism P additlonal prism Q and R of indentical shown in
fiqure. The ray will now suffer____________.
(A) greater devaition (C) total internal reflection
(B) same divaition as before (D) no devaition
43. Which of the following colours is scattered minimum ?
(A) Violet (B) red (C) blue (D) yellow
44. Angle of minimum devaition for a prism refractive index 1.5 is equal to the angle of the prism Then the
angle of prism___________
 
'
, sin 48 36 0.75given 

(A)

62
(B)

82

(C)

60
(D)

41
45. In a thin prism of glass (a
ng
= 1.5) which of the following relation between the angle of minimum
deviation
δm
and the angle of refraction r will be correct ?
(A) δ
2
m
r
 (B)
δ
2
m
r
(C) δ 1.5
m
r (D) δ
m
r
n
2
n
1
n
2
Page 9
221
46. An observer look at a tree of height 10 meters away with a telescope of magnifying power 10. To him,
the tree appears______________.
(A) 10 times taller (B) 10 times smaler (C) 10 times nearer (D) 20 times nearer
47. A normal person wants to see two pillars at a distant 11 km away separately. The distance between two
pillars should be approximately_________.
(A) 1 m (B) 3.2 m (C) 0.5 m (D) 1.6 m
48. When the length of microscope tube increases, its magnifying power________.
(A) decreases (B) increaes (C) does not change (D) none of these
49. The focal lengths of objective and the eye–piece of a compound microscpe are fo and fe raspectively.
Then___________.
(A) F
o
> F
e
(B) F
o
< F
e
(C) F
o
= F
e
(D) none of these
50. The magnifying power of a telescope is 9.0 when it is focussed for parallel rays, then the dictance
between its objective and eye–piece is 20 cm The focal lengths of lenses will be___________.
(A) 15 cm, 5 cm (B) 18 cm, 2 cm (C) 10 cm, 5 cm (D) 11 cm, 9 cm
51. A plano convex lens of f = 20 cm is silvered at plane surface New f will be___________cm
(A) 20 (B) 40 (C) 30 (D) 60
52. A ray of light from denser medium strikes a rarer medium at angle of incidence i. The reflected and
refracted rays make an angle of
90

with each other The angle of reflection and refration are r and
r '
respectively. The crictical angle is ________________.
(A) sin
–
1

(tan p) (B) tan
–
1

(tan r) (C) tan
–
1

(sin i) (D) sin
–
1
(tan r)
53. Relation between critical angle of water C
w
and that of the glass C
g

is _________. (given, n
w
= 4/3, n
g
= 1.5)
(A) C
w
< C
g
(B) C
w
= C
g
(C) C
w
> C
g
(D) C
w
= C
g
= O
54. The radius of curvature of convex surface of a thin plano–convex lens is 15 cm and refractve index of
its material is 1.6 The power of the lens will be___________.
(A) 6 D (B) 5 D (C) 4 D (D) 3 D
55. A ray of light passes through a prism having refractive index
 
n = 2
, Suffers minimum deviation If
angle of incident is double the angle of refration within prism then angle of prism is____________.
(A)
30

(B)
60

(C)
90

(D)
180

56. An air bubble inside glass slab


n =1.5
appear from one side at 6 cm and from other side at 4 cm.
Then the thikness of glass slab is____________cm
(A) 5 (B) 10 (C) 15 (D) 20
57. The magnifying power of objective of a compound microscope is 5.0 If the maginfying power of
microscope is 30, then magnifying power of eye–piece will be_________.
(A) 3 (B) 6 (C) 9 (D) 12
Page 10

Optics Notes and MCQs

Optics Notes and MCQs

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