Transcript lecture20

B. Wave optics
1. Huygens’ principle
Huygens’ principle: Every point on a wave front acts as a point source;
the wavefront as it develops is tangent to their envelope.
1) Waves Versus Particles
Huygens’ Principle and Diffraction
(qualitative descreption)
2) Huygens’ 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 wavefront and
therefore in the ray.
The frequency of the light does not
change, but the wavelength does
as it travels into a new medium.
Mirage
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
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”.
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
- constructi ve
d
m  12 
ym  R
- destructiv e
d
ym  R
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
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.
2) Dispersion of visible light
Example:
m 1
y r  3.5mm
y v  2.0mm
r  700nm
v  ?
y
R

 d
yr
r

yv
v
yv
v   r
yr
2.0mm
v  700nm
 400nm
3.5mm
Example: 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.
3) The visible spectrum and dispersion
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.
Rainbows
Actual rainbows are created by dispersion in tiny drops of water.