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Physics 202
Professor P. Q. Hung
311B, Physics Building
Physics 202 – p. 1/2
Interference and Diffraction
Interference
Light is electromagnetic waves. Shine two
light beams on a given spot and observe the
superposition of these two beams.
Physics 202 – p. 2/2
Interference and Diffraction
Interference
Light is electromagnetic waves. Shine two
light beams on a given spot and observe the
superposition of these two beams.
Superposition of two waves can lead to
constructive interference or destructive
interference.
Physics 202 – p. 2/2
Interference and Diffraction
Interference
Physics 202 – p. 3/2
Interference and Diffraction
Interference
Physics 202 – p. 4/2
Interference and Diffraction
Interference
Constructive interference:
Start with two identical sources in phase, i.e.
oscillating in the same way. If they continue to
oscillate in phase when they reach a given
point, the interference is constructive ⇒
Brightest or most intense spot. The condition
for this to be so is that their difference in path
lengths should be a integral multiple of the
wavelength.
l2 − l1 = mλ
m = 0, ±1, ±2, ...
Physics 202 – p. 5/2
Interference and Diffraction
Interference
Destructive interference: Start with two
identical sources in phase, i.e. oscillating in
the same way. If they are out of phase
(crest-to-trough) when they reach a given
point, the interference is destructive ⇒ Dark
spot. The condition for this to be so is that
their difference in path lengths should be a
half-integral multiple of the wavelength.
l2 − l1 = (m − 12 )λ
m = 0, ±1, ±2, ...
Physics 202 – p. 6/2
Interference and Diffraction
Young’s double-slit experiment
Young’s experiment demonstrated the wave
nature of light by showing that two coherent light
beams can interfere with each other.
Physics 202 – p. 7/2
Interference and Diffraction
Young’s double-slit experiment
If light were just “corpuscules”, the screen
would be illuminated just behind these two
slits.
Physics 202 – p. 8/2
Interference and Diffraction
Young’s double-slit experiment
If light were just “corpuscules”, the screen
would be illuminated just behind these two
slits.
Observation: Light is spread throughout the
screen with bright and dark fringes. ⇒ Wave
nature of light.
Physics 202 – p. 8/2
Interference and Diffraction
Young’s double-slit experiment
Huygens’s principle
Physics 202 – p. 9/2
Interference and Diffraction
Young’s double-slit experiment
Path Difference
Physics 202 – p. 10/2
Interference and Diffraction
Young’s double-slit experiment
Bright Fringes:
∆l = d sin θ = mλ
m = 0, ±1, ±2, ...
Physics 202 – p. 11/2
Interference and Diffraction
Young’s double-slit experiment
Bright Fringes:
∆l = d sin θ = mλ
m = 0, ±1, ±2, ...
Dark Fringes:
∆l = d sin θ = (m − 12 )λ
m = 0, ±1, ±2, ...
Physics 202 – p. 11/2
Interference and Diffraction
Young’s double-slit experiment
Physics 202 – p. 12/2
Interference and Diffraction
Young’s double-slit experiment: Example
Red light is used in a double-slit experiment with
the slits separated by a distance
d = 1.20 × 10−4 m. Here λ = 664 nm in vacuum.
The screen is located at a distance L = 2.75 m
from the slits. Find the distance y on the screen
between the central bright fringe and the
third-order bright fringe.
Physics 202 – p. 13/2
Interference and Diffraction
Young’s double-slit experiment: Example
The angle of the 3rd order bright fringe is
given by
(3)(664×10−9 m)
sin θ3 = 1.20×10−4 m = 0.0166.
Physics 202 – p. 14/2
Interference and Diffraction
Young’s double-slit experiment: Example
The angle of the 3rd order bright fringe is
given by
(3)(664×10−9 m)
sin θ3 = 1.20×10−4 m = 0.0166.
y = L tan θ3 ≈ 4.56 cm
Physics 202 – p. 14/2
Interference and Diffraction
Reflection of an interface
When light travels from a medium of lower
index of refraction to a region of higher index
of refraction, the reflected wave suffers a 1800
phase change.
Physics 202 – p. 15/2
Interference and Diffraction
Reflection of an interface
When light travels from a medium of lower
index of refraction to a region of higher index
of refraction, the reflected wave suffers a 1800
phase change.
When light travels from a medium of higher
index of refraction to a region of lower index
of refraction, the reflected wave suffers a no
phase change.
Physics 202 – p. 15/2
Interference and Diffraction
Reflection of an interface
Physics 202 – p. 16/2
Interference and Diffraction
Reflection of an interface: Air Wedge
Physics 202 – p. 17/2
Interference and Diffraction
Reflection of an interface: Air Wedge
Physics 202 – p. 18/2
Interference and Diffraction
Reflection of an interface: Air Wedge
Constructive interference:
Let d be the thickness of the air gap at any
point.
2 d = (m − 12 )λ
m = 1, 2, 3, ..
Physics 202 – p. 19/2
Interference and Diffraction
Reflection of an interface: Air Wedge
Constructive interference:
Let d be the thickness of the air gap at any
point.
2 d = (m − 12 )λ
m = 1, 2, 3, ..
Destructive interference:
2d = mλ
m = 1, 2, 3, ..
Physics 202 – p. 19/2
Interference and Diffraction
Reflection of an interface: Air Wedge example
A very fine wire 7.33 × 10−3 mm in diameter is
placed between two flat glass plates (see Fig.
28-9). Light whose wavelength in air is 600 nm
falls perpendicular to the plates, and a series of
bright and dark bands is seen. How many bright
and dark bands will there be? Will the area next
to the wire bright or dark?
(2)(7.33 × 10−3 mm)/(6 × 10−7 m) = 24.5.
Half-integer area next to the wire will be
bright.
Physics 202 – p. 20/2
Interference and Diffraction
Reflection of an interface: Air Wedge example
A very fine wire 7.33 × 10−3 mm in diameter is
placed between two flat glass plates (see Fig.
28-9). Light whose wavelength in air is 600 nm
falls perpendicular to the plates, and a series of
bright and dark bands is seen. How many bright
and dark bands will there be? Will the area next
to the wire bright or dark?
(2)(7.33 × 10−3 mm)/(6 × 10−7 m) = 24.5.
Half-integer area next to the wire will be
bright.
Total of 25 dark lines and 25 bright lines.
Physics 202 – p. 20/2
Interference and Diffraction
Reflection of an interface: Newton’s ring
Like an air wedge
Physics 202 – p. 21/2
Interference and Diffraction
Reflection of an interface: Thin Film
Physics 202 – p. 22/2
Interference and Diffraction
Reflection of an interface: Thin Film
Let n > 1 be the index of refraction inside the thin
film of thickness t.
Constructive interference:
2 t = (m + 12 ) λvacuum
n
m = 0, 1, 2, ..
Physics 202 – p. 23/2
Interference and Diffraction
Reflection of an interface: Thin Film
Let n > 1 be the index of refraction inside the thin
film of thickness t.
Constructive interference:
2 t = (m + 12 ) λvacuum
n
m = 0, 1, 2, ..
Destructive interference:
2 t = m λvacuum
n
m = 0, 1, 2, ..
Physics 202 – p. 23/2
Interference and Diffraction
Reflection of an interface: Thin Film and color
Physics 202 – p. 24/2
Interference and Diffraction
Reflection of an interface: Thin Film with one
phase change
Physics 202 – p. 25/2
Interference and Diffraction
Reflection of an interface: Thin Film example
A soap bubble appears green (λ = 540 nm) at a
point on its front surface nearest the viewer.
What is its minimum thickness? Assume n = 1.35
Minimum thickness ⇒ m = 0. Here we have
constructive interference.
Physics 202 – p. 26/2
Interference and Diffraction
Reflection of an interface: Thin Film example
A soap bubble appears green (λ = 540 nm) at a
point on its front surface nearest the viewer.
What is its minimum thickness? Assume n = 1.35
Minimum thickness ⇒ m = 0. Here we have
constructive interference.
t=
λ
4n
=
5.4×10−7 m
4 ×1.35
= 100 nm.
Physics 202 – p. 26/2