www.sakshieducation.com www.sakshieducation.com WAVE OPTICS Important Points: 1. The condition which allows us to use the principles of geometry is 2 b l λ >> Where b = size of the object interacting with light l = distance between the object and the screen λ = wavelength of light. 2. Two light sources are said to be coherent if they emit waves of same frequency which are in phase or which maintain a constant phase difference. 3. When two or more waves reach a point in space simultaneously, the resultant displacement at that point at any instant of time is the algebraic sum of the displacements produced by the individual waves. This is known as the principle of superposition. 4. If 2 b l << λ Fraunhofer diffraction is observed. 5. If 2 b l 2245λ Fresnel diffraction is observed 6. In interference, Resultant intensity 2 0 I 4I cos 2 φ = (Where is maximum intensity of each individual wave) φ Is initial phase difference 7. Fringe width D d λ β= 8. For two waves with intensities 1 I and 2 I with phase φ resultant intensity 1 2 12 I I I 2 I I cos = + + φ 9. When un-polarized light of intensity 0 I passes through a polarizer intensity of emergent light 0 I I 2 =
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WAVE OPTICS
Important Points:
1. The condition which allows us to use the principles of geometry is 2b lλ>>
Where b = size of the object interacting with light
l = distance between the object and the screen
λ = wavelength of light.
2. Two light sources are said to be coherent if they emit waves of same frequency which are in
phase or which maintain a constant phase difference.
3. When two or more waves reach a point in space simultaneously, the resultant displacement at
that point at any instant of time is the algebraic sum of the displacements produced by the
individual waves. This is known as the principle of superposition.
4. If 2b
l<< λ Fraunhofer diffraction is observed.
5. If 2b
l≅ λ Fresnel diffraction is observed
6. In interference, Resultant intensity
20I 4I cos
2
φ= (Where is maximum intensity of each individual wave)
φ Is initial phase difference
7. Fringe width D
d
λβ =
8. For two waves with intensities 1I and 2I with phase φ resultant intensity
1 2 1 2I I I 2 I I cos= + + φ
9. When un-polarized light of intensity 0I passes through a polarizer intensity of emergent light
0II2
=
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10. Bending of light at the edges of an obstacle or aperture is called diffraction. The phenomenon
of encroachment of light into the geometrical shadow of an obstacle is known as diffraction.
11. Diffraction is exhibited by both transverse and longitudinal waves.
12. Diffraction confirms wave nature of light.
13. Diffraction is due to the superposition of waves originating from different points of the
exposed portion of the same wave front.
14. Polarization of Light:
“The process of confining the vibrations of electric field vector of light into a single plane” is
known as polarization of light
15. Plane of Vibration or Plane of Polarization:
The plane which contains the vibrations of electric field of light (polarized light) is known as
plane of vibration or plane of polarization.
16. Law of Malus:
When the plane polarized light of intensity I 0 falls on a polarizer with an angle θ to the axis of
polarizer, then intensity of refracted light 20I I cos= θ
17. Brewster’S Law:
For polarization by reflection ptan iµ =
µ → Refractive index of reflecting surface
pi → Angle of polarization
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Very Short Answer Questions
1. What is Fresnel Distance?
A. Fresnel Distance:
The distance beyond which divergence of the beam of width ‘a’ become significant is called
Fresnel distance.
Fresnel distance 2
Fa
Z ≈λ
a = size of the aperture
λ = wave length of light
2. Give the justification for validity of ray optics?
A. Fresnel distance 2
F
aZ
λ≤ is the validity of ray optics.
If the distance between aperture and screen much smaller than i.e., 2a
λ diffraction pattern
cannot be observed so ray optics is applicable.
3. What is Polarisation of Light?
A. The phenomenon in which vibration of light vector (electric vector) are confined to a
particular direction is called polarisation.
4. What is Malus Law?
A. Malus Law:
The intensity of polarized light transmitted through the analyzer varies as the square of the
cosine of the angle between the plane of transmission of the polarizer and analyzer.
I = I0cos2 θ Where θ is the angle between the axis of the polarizer and analyzer.
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5. Explain Brewster’s Law.
A. Brewster’s Law:
The tangent of the angle of polarisation is equal to the refractive index of the reflecting
medium.
pTaniµ =
At polarising angle the reflected ray and refracted ray are perpendicular to each other.
6. When does a monochromatic beam of light incident on a reflective surface get completely
transmitted?
A. If 2
F
aZ
λ= then diffraction pattern is not observed then monochromatic beam of light incident
on a reflective surface gets completely transmitted.
Short Answer Questions
1. Explain Doppler Effect in light. Distinguish between Red Shift and Blue Shift?
A. Doppler Effect Light:
The apparent change in the frequency due to relative motion between the source and observer is
called Doppler Effect.
If ‘v’ is the actual frequency and ‘'ν ’ is the apparent frequencies, then the relative change in
frequency
v
c
∆ν = −ν
v
or c
∆λ =λ
Here ‘c’ is the speed of light and ‘v’ is the velocity of the source which is small compared to
that of light. Doppler Effect in light is symmetric.
Red Shift and Blue Shift: - Apparent wavelength > Actual Wavelength.
Hence the spectrum of the radiation from the source of light shifts towards the red end of
spectrum. When a star is moving away from the Earth the wavelength increases and it looks
more reddish. This is red shift phenomenon. When the waves are received from a source
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moving towards the observer, there is an apparent decrease in wavelength. This is called blue
shift.
2. What is total internal reflection? Explain the phenomenon using Huygens principle?
A. Let XY be a surface separating the two media (1) and (2) of refractive indices 1µ and 2µ
respectively and let V1 and V2 be the speed of light waves in medium (1) and medium (2)
respectively. Let AC be a plane wave front incident on XY. Lines AA1and CC1 which are
normals to the incident plane wave front (i.e., AC) are called incident rays.
Huygens’principle:
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If CN is the normal at the point C, then 'C CN i∠ = (angle of incidence). Angle of incidence is
also the angle which the incident plane wave front makes with the plane XY, i.e. ACY i∠ = .
The points A and C on this wave front will serve as the sources of disturbance and will give out
secondary wavelets. During the time the secondary wavelet from A strikes the surface XY at D,
the secondary wavelet from C would have travelled a distance CE in the medium-2 where the
distance CE is such that time taken by the secondary wavelet to travel a distance AD in the
medium-1 = time taken by the secondary wavelet to travel a distance CE in the medium-2.
i.e.
1 2
AD CE
V V= (As time = distance/velocity)............ (i)
Total Internal Reflection
We have seen that the radius of the secondary spherical wavelet from C in medium-2 given by
equation. (1)
1
2
AD V
CE V= or 2
1
VCE AD
V= ×
1
2
sinCE CD iµµ
=
as sinAD
iCD
=
CE > CD . In this case if a hemispherical wavelet is drawn with C as centre, the point D will lie
inside this wavelet. Since no tangent plane can be drawn from D to this wavelet. Since no
tangent plane can be drawn from D to this wavelet, there is no refracted plane wave front which
implies that no refraction is possible. But a reflected wave front in the medium-1 is possible.
This is due to the reason that the radius of the reflected hemispherical wavelet from C is equal
to 'CE (which is less than CD). This situation corresponds to total internal reflection.
3. Derive the expression for the intensity at a point where interference of light occurs.
Arrive at the conditions for maximum and zero intensity?
Interference:
A. The redistribution of energy due to super imposition of two or more waves is called
interference.
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Derivation for Interference Pattern:
Consider two waves coming from S1 and S2
They interfere at a point ‘P’ on the screen. Their equations are given by
1 sinY a tω=
( )2 sinY a tω φ= +
Where φ is the phase difference between two waves
S
G
G1
O
DS2
S1
P
Z
x
yz
The resultant wave equation is given by
1 2Y Y Y= +
( )sin sinY a t a tω ω φ= + +
[ ]sin sin cos cos sina t a t tω ω φ ω φ= + +
= ( )sin 1 cos cos sina t a tω φ ω φ+ +
Let ( )1 cos cosa Rφ θ+ = ------ (1)
sin sina Rφ θ= ------ (2)
sin cos sin cosY R t R tω θ θ ω= +
( )sinR tω θ= +
The above equation represent’s S.H.M and its amplitude is R