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B. Wave optics
1. Huygens’ principle
Every point on a wave front acts as a point source;
the wave front as it develops is tangent to their envelope.
1) Waves versus particles
Huygens’ principle and diffraction
(qualitative description)
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2) Huygens’s Principle and the Law of Refraction
As the wavelets propagate from
each point, they propagate more
slowly in the medium of higher
index of refraction. This leads to
a bend in the wave front and
therefore in the ray.
sin 1  v1t / AD
sin  2  v2 t / AD
sin 1 v1 n2



sin  2 v2 n1
The frequency of the light does not change,
but the wavelength does as it travels into a
new (linear) medium.
1 v1T v1 / f n2



2 v2T v2 / f n1
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Question: What is changed, when a light wave enters into a medium of
different optical density?
A) its speed and frequency
B) its speed and wavelength
C) its frequency and wavelength
D) its speed, frequency & wavelength
3) Mirage
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2. Interference
Interference – combination of waves
(an interaction of two or more waves arriving at the same place)
Important: principle of superposition
Valley
Peak
(b)
(a)
Valley
Waves source
(b)
(a)
No shift or shift by
r2  r1   m
Shift by
r2  r1  m  12 
m  0,1,2,...
(a) If the interfering waves add up so that they reinforce each other, the total
wave is larger; this is called “constructive interference”.
(b) If the interfering waves add up so that they cancel each other, the total
wave is smaller (or even zero); this is called “destructive interference”.
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3. Young’s experiment (Double-Slit Interference)
d sin 
Depending on the path length difference
between the slits and the screen, the wave
can interfere constructively (bright spot) or
destructively (dark spot).
d sin  m   m - constructi ve
d sin  m  m  12  - destructiv e

m  0,1,2,..
R
  m
y m  R tan  m  R sin  m 
m
ym  R
- constructi ve
d
m  12 
ym  R
- destructiv e
d
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Example: In a double-slit experiment, it is observed that the distance between
adjacent maxima on a remote screen is 1.0 cm. What happens to the distance
between adjacent maxima when the slit separation is cut in half?
A) It increases to 2.0 cm.
B) It increases to 4.0 cm.
C) It decreases to 0.50 cm.
D) It decreases to 0.25 cm.
Example: Monochromatic light falls on two very narrow slits 0.048 mm apart.
Successive fringes on a screen 5.00 m away are 6.5 cm apart near the center
of the pattern. What is the wavelength of the light?
d  0.048mm
R  5.00m
y1  6.5cm
 ?
m
ym  R
- constructi ve
d
y1
d
R
2
6
.
5

10
m
  0.048  10 3 m
 624.10 9 m  624nm
5.00m
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4. Dispersion
1) Dispersion in Young’s experiment
Since the position of the maxima (except the central one) depends on
wavelength, the first- and higher-order fringes contain a spectrum of colors
Question: The separation between adjacent maxima in a double-slit
interference pattern using monochromatic light is
A) greatest for red light
B) greatest for green light
C) greatest for blue light
D) the same for all colors of light
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Example:
m 1
y r  3.5mm
y v  2.0mm
r  700nm
v  ?
y
R

 d
yr
r
v  700nm

yv
v
yv
v   r
yr
2.0mm
 400nm
3.5mm
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2) Dispersion in prism
The index of refraction of a material
varies somewhat with the wavelength
of the light.
This variation in refractive index
is why a prism will split visible
light into a rainbow of colors.
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Rainbows
Actual rainbows are created by dispersion in tiny drops of water.
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