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IV. Optics
Nature of light. Spectrum of electromagnetic waves.
Wavelength decreases 
Frequency increases 
Note: 1 nanometer = 10-9 meter
A. Geometric optics
1. Wave front and rays
rays
wave fronts
normal to
surface
2. Reflection
in
1   2
1 2
out
1 2
diffuse reflection
3. Refraction: Snell’s Law
n1 sin 1  n2 sin 2
index of refraction:
n1 v2 2
 
n2 v1 1
f1  f 2
Example:
1
n1
n
c
v
1
2
n1 sin 1  n2 sin  2  n3 sin 3
 2 2
n2
n3
3
 3 is independen t from n2
If n3  n1  3  1
Example:
n1  1.00
n2  1.33
1  50
2  ?

n1 sin 1  n2 sin 2
 
n1
1.00
sin  2  sin 1 
sin 50  
n2
1.33
 2  35 
Example: Equilateral triangle
n1  n4  1.00
n2  n3  n  1.52
1  45
4  ?
n=1.52
n1 sin 1  n2 sin  2
 2   3  60
n3 sin  3  n4 sin  4

 2  27.7 
 3  32.3
 4  54.3
sin 1  n sin  2
 2   3  60
n sin  3  sin  4
sin 1
sin  2 
n
 3  60   2
sin  4  n sin  3
4. Total internal reflection
n1
1
n2  n1
2
n2
2
n1  n2
1
0  1  90  0  sin 1  1
0   2  90  0  sin  2  1
n1
n1
0  sin  2  sin 1   1
n2
n2
n2
n2
0  sin 1  sin 1   1
n1
n1
0   2  C
0  1   C
n2
sin  C 
n1
Example:
n2 1
1
 
n1 n 1.52
n1  n  1.52
sin  C 
n2  1.00
 C  41.1
C  ?
Example: A ray of light is incident in air on a block of a transparent solid
whose index of refraction is n. If n =1.38, what is the largest angle θ1 for which
total internal reflection will occur at the vertical face (point A)?
1
1
n
 2  90    3
sin  3 
2
A
sin 1  n sin  2
3


sin 1  n sin 90   3 
1
 n cos  3  n 1  sin  3  n 1  2  n 2  1
n
2
sin 1 
1.382  1  0.95
1  72
n=1.38
Example:
1
sin  C 
n
C

α
α
n=1.52

sin 90   
α
1
n
1
1
cos   
n 1.52
  49
4a. Applications of total internal reflection
1) Binoculars often use total internal
reflection; this gives true 100% reflection,
which even the best mirror cannot do.
2) Fiber optics. Light will be transmitted along the fiber even if it is not
straight. An image can be formed using multiple small fibers.
5. Plane mirror
O




do
di
do
I
O


do = di
di

I
Image:
virtual
erect
the same size
This is for plane
mirrors
6. Comments about objects and images
created by different optical instruments
(curved mirrors, lenses and their combinations)
Image:
real or virtual
erect or inverted
lager, smaller, or the same size as the object