# Lecture 31 - McMaster Physics and Astronomy

Physical Optics Ch 37 and 38
Physical Optics
Light is an electromagnetic wave.
Wave properties:
Diffraction – wave bends around corners,
Interference – waves from two or more
sources interfere
Electromagnetic Waves
  
E , B, v all 
Eo
E
B
v
Usually we keep track of the electric field E :


E( x, t )  Eo sin( kx  t )
amplitude
The Electromagnetic Spectrum
l (m)
300
3
3 x 10-3
10-6
3x
7 x 10-7
4 x 10-7
3x
10-9
3x
10-12
f (Hz)
TV
Microwave
Infrared
Visible
Ultraviolet
X rays
g rays
106
108
1011
1014
5x1014
1017
1020
Infrared
Red
780 nm
Yellow
600 nm
Green
550 nm
Blue
450 nm
Violet
Ultraviolet
380 nm
Infrared
Red
l
780 nm
Yellow
600 nm
Green
550 nm
Blue
450 nm
Violet
Ultraviolet
380 nm
Visible-Light
Spectrum
The EM Spectrum
Coherent sources are sources that have a constant phase
difference between them (lasers).
In phase sources are sources that have zero
phase difference between them.
Monochromatic sources have the same wavelength.
Plane waves mean the wavefronts are planes
Wavefronts are surfaces on which we have only crests,
or troughs for example.
Double Slit
(Thomas Young, 1801)
θ
incident
light,plane
waves
Two slits,
separation d
m=2
m=1
m=0
m=-1
m=-2
screen
Result: Many bright and dark fringes or lines on
the screen:
The slits act as sources of light in phase. Due to
diffraction, the light spreads out after it passes
through each slit. When the two waves arrive together
at some point P on the screen, they are out of phase,
due to the difference in the length of the paths. This
path difference varies from place to place on the
screen.
P
x1
x2
d
q
x  x2  x1  d sin q
screen
Constructive Interference: (bright fringe)
Δx = mλ,
or
d sin θ = mλ, m = 0, 1, 2, …
Destructive Interference: (dark fringe)
Δx = (m + &frac12;)λ,
or
d sin θ = (m + &frac12;) λ, m = 0, 1, 2, …
Example 1
2 slits, 0.20 mm apart;
red light (l = 667 nm)
y
0
3m
screen
Where are a) the m=0,1 bright fringes?
b) m=0,1 dark fringes?
(give values of y)
Solution
Example 2
2 slits, red light (l = 690 nm)
y
50 cm
0
screen
If the distance between the first and the third
minima in the diffraction pattern is 3.0mm,
what is the width of the slit?
Solution
Quiz
Which of the following would cause the separation
between the fringes on the screen to decrease?
(There may be more than one answer.)
A)
B)
C)
D)
E)
F)
Increasing the wavelength
Decreasing the wavelength
Moving the slits closer together
Moving the slits farther apart
Moving the screen further from the slits
Moving the screen closer to the slits
Test Discussion