PHYS 260 Lecture Notes - Lecture 3: Fraunhofer Diffraction, Optical Instrument, Waveplate
25 May 2018
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UNIT-1 PHYSICAL OPTICS FOR INSTRUMENTS
INTERFERENCE: Introduction – Interference in thin films by reflection – Newton‟s rings.
DIFFRECTION : Introduction – Fraunhofer diffraction - Fraunhofer diffraction at double slit (qualitative) –
Diffraction grating – Grating spectrum – Resolving power of a grating – Rayleigh‟s criterion for resolving
power.
POLARIZATION : Introduction – Types of Polarization – Double refraction – Quarter wave plate ad Half
Wave plate.
SUPERPOSITION OF WAVES
1) Super position of waves of equal Phase and frequency
Let us assume that two sinusoidal waves of the same frequency are travelling together in a medium. The
waves have the same phase without any phase angle difference between them. Then the crest of one wave
falls exactly on the crest of the other wave and so do the troughs. The resultant amplitude is got by adding
the amplitudes of each wave point by point. The resultant amplitude is the sum of the individual
amplitudes A = A1 +A2 + ---
The resultant intensity is the square of the sum of the amplitudes
I = ( A = A1 +A2 + ---)2
2) Superposition of waves of constant phase difference
Let us consider two waves that have the same frequency but have a certain constant phase angle
difference between them. The two waves have a certain differential phase angle. In this case the crest of
one wave does not exactly coincide with the crest of the other wave. The resultant amplitude and intensity
can be obtained by trigonometry.
The two waves having the same frequency and a constant phase difference () can be represented
by the equations
Y1 = a sin and Y2 = asin(+) where is the constant phase difference a the amplitude and is
the angular frequency of the waves. The resultant amplitude Y is given by Y =Y1 +Y2
= a sin + a sin(+) = a sin + a(+)
= a sin + a+
=(a+a) + a ---(1)
If R is the amplitude of the resultant wave and is the phase angle then Y =R sin(+)
=R{sin + }
=R +R sin -----(2)
Comparing equations(1) and (2)
R = a(1+)------(3)
R sin = a ---------- (4)
Squaring and adding equations (3) and (4)
+=+(1 + cosφ)
= 2(1 + )= 2. 22
= 42
INTERFERENCE IN PLANE PARALLEL FILMS DUE TO
REFLECTED LIGHT
Let us consider a plane parallel film. Let light be incident at A part of the light is reflected towards R1 and
the other part is refracted into the film towards B. this second part is reflected at C and emerges as R2 and
is parallel to the first part.
at normal incidence, the path difference between ray 1 and ray 2 is twice the optical thickness of
the film.
Δ = 2µt
At oblique incidence the path difference is given by Δ = µ(AB+BC) – AD
=
− [cosr =
=
=
=BC]
=
−2. [∵ = = 2. = 2.]
A
B
C
D
E
R
1
R
2
i.e., Δ =2{
−} = 2{
} = 2.cosr which is known as
cosine law.
where is the refractive index of the medium between the surfaces since for air =1,the path
difference between ray1 and 2 is given by Δ = 2.cosr.
it should be remembered that a ray reflected at a surface backed by a denser medium suffers an abrupt
phase change of π which is equivalent to a path difference /2
thus the effective path difference between the two reflected rays is( 2.cosr± /2)
we know that maxima occurs when effective path difference Δ = n
i.e., 2.cosr± /2 = n
if this condition is fulfilled, the film will appear bright in the reflected light.
COLOURS OF THIN FILMS
Sun light reflected by thin films of oil on water or soap bubbles exhibit beautiful colours. These colours
are due to interference between light waves reflected from the upper and lower surfaces of thin films.
A thin transparent film of uniform thickness ‘t’. A parallel beam of light is incident at an angle i on the
upper surface. Due to multiple reflections and refractions in the film the incident light beam is split into
(a) the reflected and (b) refracted waves.
Reflected waves API, CPI,EPI etc, interference at PI to produce a resultant interference pattern at PI.
Similarly refracted waves BP,DP,FP etc combine to form interference pattern at P.
P
P
1
A C E
F
D
B
i
r
t
Document Summary
Interference: introduction interference in thin films by reflection newton s rings. Diffrection : introduction fraunhofer diffraction - fraunhofer diffraction at double slit (qualitative) . Diffraction grating grating spectrum resolving power of a grating rayleigh s criterion for resolving power. Polarization : introduction types of polarization double refraction quarter wave plate ad half. Superposition of waves: super position of waves of equal phase and frequency. Let us assume that two sinusoidal waves of the same frequency are travelling together in a medium. The waves have the same phase without any phase angle difference between them. Then the crest of one wave falls exactly on the crest of the other wave and so do the troughs. The resultant amplitude is got by adding the amplitudes of each wave point by point. The resultant amplitude is the sum of the individual amplitudes a = a1 +a2 + --- The resultant intensity is the square of the sum of the amplitudes.
