Physics Paper II for HSC students

1. Physical Optics
Animesh Samundh
by

2. Geometrical Optics deals with particle nature of light.
Physical Optics deals with wave nature of light.

3. Clark
Maxwell
first
established
that EM
wave is not
a
mechanical
wave.
In 1831,
Michael
Faraday
invented EM
induction.

4. In 1864, James Clark Maxwell proposed
opposite effect of Faraday.

5. If alternate electric field vector (𝐸) and magnetic field vector
(𝐵)vibrates perpendicularly then a wave perpendicular on
both (𝐸) and (𝐵) propagates at 3X108 ms-1 which is called
electromagnetic wave.
Speed of this wave, C = f𝜆

6. In vacuum, if c = speed of light,
E0 = peak value of electric field
B0 = peak value of magnetic field
In t sec, E = E0 sin (x – ct)
B = B0 sin (x – ct)

7. From Maxwell’s theory, E0 = CB0
Magnitude of c in vacuum for all types of EM
wave is constant which not only depends on
λ and f.

8. Heinrich Hertz in 1888 produced an EM wave of small wave
length from an oscillated electric coil.
Marconi researched in the field of radio broadcasting.

9. Characteristics of EM wave:
- In vacuum its speed is 3X108 ms-1.

10. Pointing vector:
EM wave can transfer energy from one point to another.
Amount of energy passing through a unit area
perpendicular to the motion of EM wave is called Poyinting
vector.
Its denoted by S.

11. Radio 10-1m to 105
Oscillating electric circuit
Small change in energy in the
electron of an atom
Radio
communication
Compare seven EM waves
Wave Range of 𝝀 Source Cause Uses
Micro 10-1m to 10-3
IR 10-3m to 4X10-7
Visible 3.9X10-7m to 7.8X
10-7
UV 3.9X10-7m to
3X10-9 m
X – ray 3.9X10-9m to
10-11
Gamma 10-11m to 10-15

12. Disturbance which transforms energy without displacing
the particles is called wave.

13. Wave front: What is wave front?
The locus of the particle of a wave having same phase is called
wave front.

14. A surface touching these secondary wavelets tangentially in the
forward direction at any instant gives the new wave front at
that instant. This is called secondary wave front

15. Wave front is of two types:

16. b) Plane wave front: If the locus of the particles in a wave having same
phase is plane, then the wave front is plane wave front.
a) Spherical wave front: If the locus of the particles in a wave having
same phase is spherical, then the wave front is spherical wave front. As
the distance from the origin of waves goes on increasing, the curvature of
the spherical wave front goes on decreasing. At a large distance from the
source, the wave front becomes very nearly plane like shape.

17. Huygens's principle:
To explain interference, diffraction and polarization Huygen gave two
assumption as:
1. Each point on a wave front is a source of a new disturbance called
second wave which travels with the same velocity as that of original
waves’ provided the medium is same.

18. Huygens's principle:
2. The position and the shape of the new wave front at any instance of
time t is given by the envelope or tangential surface of the secondary
wavelets at that instance.

19. Explanation: Suppose for the source S, AB is a spherical wave front.
According to Huygens’s principle each point of AB will be a secondary
source. In the diagram, P1, P2, P3 etc are secondary source.

20. Application of Huygens's Principle:
Law of reflection:

21. Law of refraction:

22. Super Position of waves:

23. Same & opposite Phase

24. Coherent source: The sources of light which emits continuous
light waves of the same wavelength, same frequency and in same
phase or having a constant phase difference are called coherent
sources.
Laser light is highly coherent and monochromatic.

25. Interference of Light.

26. Interference Fringe

27. Conditions for Interference
• Sources should be coherent.
• Sources should be very fine and small
• Sources should be very close to each other
• Amplitude of the two sources should be very close to each
other
• For alternate bright and dark points, the path difference
between the waves should be even & odd multiples
respectively.

28. Characteristics of Interference
• Interference is produced when two coherent sources
superposed at a point in a medium.
• Normally the width of the interference fringes are equal.
• Distance between the bright & dark fringes are equal.
• The intensity of all the bright fringes are equal

29. Relation between phase difference & Path difference
𝛿 =
2𝜋
𝜆
𝑥

30. Phase Difference

31. Constructive Destructive
Def (i) When the waves meets
a point with same phase,
constructive interference
is obtained at that point
(i.e. maximum light)
i) When the wave meets a
point with opposite phase,
destructive interference is
obtained at that point (i.e.
minimum light)
Phase
difference
ii) φ = 00 or 2nπ ii) φ = 1800 or (2n – 1) π;
n = 1, 2, ….
Or, (2n+1)π; n = 0, 1, 2
…….
Two Types of Interference

32. Young’s Double Slit Experiment

33. Young’s Double Slit Experiment

34. Mathematical Analysis of Young’s Double Slit
Experiment
y1 = a sin
2𝜋
𝜆
vt
y2 = a sin
2𝜋
𝜆
(vt+x)
y = a sin
2𝜋
𝜆
vt + a sin
2𝜋
𝜆
(vt+x)
y = 2a cos
𝜋𝑥
𝜆
vt
Bright fringe & Dark fringe
O
Q
R
x
P
Screen
S1
S2
d
D

35. Fringe gap and Fringe width
PQ = x -
𝒅
𝟐
& PR = x +
𝒅
𝟐
S2P2 – S1P2
= 𝐃 𝟐
+ x +
𝐝
𝟐
𝟐
− 𝐃 𝟐
+ x −
𝐝
𝟐
𝟐
= 𝟐𝐱𝐝
S2P – S1P S2P + S1P = 𝟐𝒙𝒅
S2P – S1P =
𝟐𝒙𝒅
S2P + S1P
=
𝟐𝒙𝒅
𝟐𝑫
As S2P ≈ S1P ≈ D
O
Q
R
x
P
Screen
S1
S2
d
D

36. Path difference,
S2P – S1P =
𝟐𝒙𝒅
𝟐𝑫
=
𝒙𝒅
𝑫
For maximum brightness at P
𝒙𝒅
𝑫
= 𝒏𝝀
Here, n = 0, 1, 2, 3, ……
For central max, n = 0

37. From O to any side, for first, second, third etc. bright fringe
n = 1, 2, 3 etc.
If from O to nth bright fringe is xn then
𝒙 𝒏 𝒅
𝑫
= 𝒏𝝀
Or, 𝐱 𝐧 = 𝐧
𝛌 𝐃
𝐝
For (n+1)th bright fringe from O , 𝐱 𝐧+𝟏 = (𝐧 + 𝟏)
𝛌 𝐃
𝐝
Difference between two consecutive bright fringe,
𝐱 𝐧+𝟏 − 𝒙 𝒏 = 𝐧 + 𝟏
𝛌 𝐃
𝐝
− 𝐧
𝛌 𝐃
𝐝
=
𝛌 𝐃
𝐝

38. Similarly Path Difference between
two consecutive dark fringe,
𝐱 𝐧+𝟏 − 𝒙 𝒏 =
𝛌 𝐃
𝐝
Fringe width
Fringe width
Dark
fringe
Bright
fringe
Fringe gap
So, Fringe width,
x =
𝛌 𝐃
𝟐𝐝
This equation is used when one fringe is
mentioned

39. About interference
• For interference, distance between the centre of two bright or dark
fringe or fringe width are same
• The more the D value the more the fringe width
• The less the ‘d’ the more the fringe width

40. Diffraction

41. Diffraction:
Fresnel diffraction Fraunhofer diffraction
(i) If either source or screen or both are at
finite distance from the diffracting device
(obstacle or aperture), the diffraction is
called Fresnel type.
(ii) Common examples : Diffraction at a
straight edge, narrow wire or small opaque
disc etc.
(i) In this case both source and screen
are effectively at infinite distance from
the diffracting device.
(ii) Common examples : Diffraction at
single slit,
double slit and diffraction grating

43. a sinθ = (2n + 1) λ/2
For a bright point from edge
S1 and S2
a sinθ = nλ
And for a dark point from
edge S1 and S2
a θ
θ
S1
S2

44. Diffraction Grating
The special device for the production of diffraction is called Grating.
It consists of a very large number of narrow slits of equal width side
by side.
Grating Constant, d = a + b
Distance from the starting
of a slit to the starting of the
next slit is called Grating
Constant

45. In the length ‘d’ of the grating, number of line = 1
So, the number of lines in unit length,
N =
1
𝑑
=
1
𝑎+𝑏

46. Polarization of light

47. Polarization of Light

48. Some Terms related to Polarization of
Light
• Polarized Light
• Unpolarized Light
• Plane Polarized Light
• Plane of vibration
• Polarising angle
• Plane of Polarization
• Double refraction
• Optic axis
• Principal plane
• Principal section

49. Important Mathematical Problems
Type 1: Electromagnetic Wave
E = E0sin(x – ct)
Equation to be used
B = B0sin(x – ct)
Relation between electric & magnetic field,
Bo =
𝑬 𝒐
𝒄

50. Type 2: Light speed
C = f𝜆 =
1
∈0 𝜇0
Type 3: Light speed, wave length & RI
a 𝜇b=
𝐶 𝑎
𝐶 𝑏
=
𝜆 𝑎
𝜆 𝑏
a 𝜇b=
𝜇 𝑏
𝜇 𝑎

51. Speed of light in water is 2.22X108 ms-1. wavelength of sodium
light in vacuum is 5892 Å then determine wavelength of that
light in water.
Hints:
𝑪 𝟎
𝑪 𝒘
=
𝝀 𝟎
𝝀 𝒘

52. Path difference between two points of a wave is
5𝜆
2
then determine the
phase difference. 𝝅
Type 4: Phase difference & path difference
Hints: 𝛿 =
2𝜋
𝜆
𝑥
Phase difference between two points of a wave is
𝜋
2
then determine
path difference.
𝝀
𝟒

53. Type 5: distance between central bright to nth fringe
𝒙 𝒏 =
𝒏𝑫𝝀
𝒅
Where, n = number of fringe
D = distance between the slit & the screen
𝜆 = wavelength
d = distance between two slits
This equation may be used to determine distance from central max to any
fringe, screen distance, wavelength, distance between two slits, no. of fringe
Type 6: width of the bright fringe
𝚫𝒙 =
𝑫𝝀
𝟐𝒅

54. Mathematical problems
• In a Young’s double slit experiment, distance between two slits is
0.4mm. At 1m distance a fringe is created where the distance
between the central max to 12th bright fringe is 9.3mm. Determine
the wavelength of the wave.
[3100 Å]
• In a Young’s double slit experiment, the separation between the slits is
0.10 m, the wavelength of light used is 500 nm and the interference
pattern is observed on a screen 1.0m away. Find the separation between
successive bright bands. 𝒙 =
𝑫𝝀
𝒅

55. • In a Young’s double slit experiment, fringe width is found is 0.4mm.
Keeping the arrangement same if the experiment is done in water then
what will be the fringe width? Refractive index of water is
𝟒
𝟑
• 𝝁 𝒘 =
∆𝒙
∆𝒙/ where, ∆𝒙/
is the new fringe width

56. An interference spectra is formed in the screen at a distance of
1m from two slits having separation of 0.4 mm. If the
wavelength of light is 500 Å then
a) Find the distance between two successive bright bands and
b) What is the distance between two successive dark bands.
a)
b) 2x

57. Find 2d
A double slit experiment is performed with light of wavelength
589nm and he interference pattern is observed on a
screen 100 cm away. The tenth bright fringe has its centre at a
distance of 10 mm from the central maximum. Find the
separation between the slits

58. Condition for bright point: a sin𝜽 = (𝟐𝒏 + 𝟏)
𝝀
𝟐
Type 4: Diffraction
Condition for dark point: a sin𝜽 = 𝒏𝝀
These equations are used to determine width of the slit, number of
fringe, diffraction angle and wavelength
For grating constant: d sin𝜽 = 𝒂 + 𝒃 𝒔𝒊𝒏𝜽 =
𝒔𝒊𝒏𝜽
𝑵
= 𝒏𝝀
Where, N =
𝟏
𝒂+𝒃

59. In a Fraunhauffer class diffraction experiment due to a single
slit a light of wavelength of 5600Å is used. Determine the
angle of diffraction for the first dark band. [width of the slit
= 0.2 mm]
We know,
a sinθ = nλ
Ans: 0.160

60. In a Fraunhauffer class diffraction light of wavelength of 5600Å
is used. Find the angle of diffraction of the second maxima
a sinθ = nλ
θ = 300

61. A light of wavelength of 8X10-7 m incident on a plane grating
produces the angle of diffraction of 300 for the first order. What
is the number of lines per cm in the grating?

62. There are 4200 lines per cm in a grating. If parallel rays of
sodium light are incident normally on it, then the second order
spectral lines produces an angle of 300. Calculate the
wavelength of sodium light
We know, (a+b)Sinθn = nλ
λ = 595 m

63. 1. In optics lab, Raihan incident a monochromatic light of 600 nm
through a 2μm wide slit perpendicularly. H thought that he would
see nine bright points.
c) Determine angular distance between first order bright points.
d) Analyze whether he could see nine bright points or not!

64. 2. In a Young’s double slit experiment distance between the slits is
0.3mm. Distance from the slit to the screen is 1m. While experimenting
in air, distance between the central maxima to 8th bright fringe was
found 6.2mm. The whole system is kept in water.
c) Determine wavelength of light used in the experiment.
d) In water, will there be any change in fringe width? Analyze.

65. 3. In Young’s double slit experiment following arrangement is shown.
Wavelength of the light used 5800 Ǻ
1m
2mm
20cm
c) Determine the wavelength of light used I the stem.
d) If the screen distance is increased by 20 cm then will you get the fringe
of same width? Analyze.

66. 1. Electromagnetic wave
2. Wave theory of light
3. Electromagnetic theory
4. Poynting vector
5. Wave front
6. Diffraction grating
7. Plane transmission grating
8. Grating constant
9. Polarized Light
10.Unpolarized Light
11.Plane Polarized Light
12.Plane of vibration
13.Polarising angle
14.Plane of Polarization
15.Double refraction
16.Optic axis
17.Principal plane
18.Principal section

67. 1. Compare 7 electromagnetic waves.
2. Write down the characteristics of electromagnetic waves.
3. What do you mean by 1 light year?
4. State Huygens’s principle of formation of wave front.
5. What is interference of light? Write down the conditions and
characteristics of interference of light.

68. 6. Write down the difference between constructive and
destructive interference.
7. What do you mean by coherent source?
8. Show relation between phase difference and path difference.
9. What is diffraction of light? Write down the condition for
diffraction of light.

69. 10. Write down the difference between Fraunhoffer and Fresnel
Class diffraction.
11. Write down the difference between Interference and
diffraction.
12. Two same type of light source can’t produce interference –
explain.
13. If a thin glass plate is placed on the path of one source then will
there be any change in fringe? Explain your answer.
14. Longitudinal waves have no polarization – Explain.

70. 15. Light year through glass is 6.27X1012 km – What do you mean
by this?
16. No source is coherent in nature – Explain.

71. Facts for MCQ
19. When the waves are coherent?
20. Conditions for interference of light.
21. When two coherent monochromatic light source forms
constructive interference then phase difference becomes
__________
22. What is the reason for keeping two slits in case of Young’s
double slit experiment?
23. Phase difference between the two points of a wave is
𝜋
2
then path difference between the point will be _______

72. Comparison between different Light
Theory

73. Sl. No. Phenomena Corpuscular Wave EM wave Quantum Dual
1. Rectilinear
Propagation
√ √ √ √ √
2. Reflection √ √ √ √ √
3. Refraction √ √ √ √ √
4. Dispersion X √ √ X √
5. Interference X √ √ X √
6. Diffraction X √ √ X √
7. Polarization X √ √ X √
8. Photoelectric
effect
X X X √ X