Today’s agenda:
Introduction to Light.
You must develop a general understanding of what light is and how it behaves.
Reflection and Refraction (Snell’s Law).
You must be able to determine the path of light rays using the laws of reflection and
refraction.
Total Internal Reflection and Fiber Optics.
You must be able to determine the conditions under which total internal reflection occurs,
and apply total internal reflection to fiber optic and similar materials.
Dispersion.
You must understand that the index of refraction of a material is wavelength-dependent.
Reflection
Light striking a surface may be reflected, transmitted, or
absorbed. Reflected light leaves the surface at the same angle
it was incident on the surface:
i = r
i r
Real Important Note: the angles are measured relative to the surface normal.
Possible homework hint: the sum of the angles in a 4-sided polygon is 360.
Reflection from a
smooth surface is
specular (mirrorlike). Reflection
from a rough
surface is diffuse
(not mirror-like).
http://acept.la.asu.edu/PiN/rdg/reflection/reflection.shtml
http://www.mic-d.com/java/specular/
Refraction
Light travels in a straight line
except when it is reflected or
when it moves from one
medium to another.
http://id.mind.net/~zona/mstm/physics/light/rayOptics/refraction/refraction1.html
Refraction—the “bending,” or change of direction of light rays
when light moves from one medium to a different one—takes
place because light travels with different speeds in different
media.
The speed of light in a vacuum is c = 3x108 m/s. The index of
refraction of a material is defined by
c
n =
,
v
If you study light in advanced classes,
you’ll find it is more complex than this.
where c is the speed of light in a vacuum and v is the speed of
light in the material.
The speed and wavelength of light change when it passes
from one medium to another, but not the frequency, so
c

v=
and n = .
n
n
Because light never travels faster than c, n  1.* For water, n =
1.33 and for glass, n 1.5. Indices of refraction for several
materials are listed in your text.
Example: calculate the speed of light in diamond (n = 2.42).
c
v =
n
3×108 m/s
v =
2.42
v = 1.24×108 m/s
*Actually, not true but don’t worry about it unless you take advanced courses in optics.
Because n  1, we
see this:
If n < 1, we would
see this:
Thanks to Dr. Xiaodong Yang for the images.
Snell’s Law
When light moves from one medium into another, some is
reflected at the boundary, and some is transmitted. “Toy”
The transmitted light is refracted (“bent”).
a is the angle of incidence, and b is the angle of refraction.
a
b
air (na)
water (nb)
water (na)
b
nb>na
air (nb)
a
na>nb
na sin  θa  = nb sin  θb 
Light passing from air (n  1) into water (n  1.33).
Light “bends” towards the normal to the surface as it slows
down in water.
a
air (na)
water (nb)
b
(1)  sin  θa   = (1.33)  sin θb  
θa > θb
nb>na
na sin  θa  = nb sin  θb 
Light passing from water (n  1.33) into air (n  1).
Light “bends” away from the normal to the surface as it
speeds up in air.
(1.33)  sin  θa   = (1)  sin  θb  
b
air (nb)
water (na)
θa < θb
a
na>nb
na sin  θa  = nb sin  θb 
Snell’s law, also called the law of refraction, gives the
relationship between angles and indices of refraction:
na sin  θa  = nb sin  θb  .
air (na)
air (na)
a
a
b
water (nb)
b
water (nb)
You are free to choose which is “a” and which is “b.”
 is the angle the ray makes with the normal!