Refraction
Changing Speed
 The speed of light in a material
depends on the
electromagnetic properties.
• Permittivity and permeability
 The ratio of the speed in a
material to that of a vacuum is
the index of refraction.
n
c
v
Clear Media
 Every transmitting medium has
its own index of refraction.
 Air
1.00029
 Ice
1.31
 Water
1.333
 Alcohol
1.36
 Quartz
1.4584
 Plexiglas
1.51
 Crown glass 1.52
 Flint glass 1.66
 Zircon
1.923
 Diamond
2.417
• Values at 589 nm
Refraction Geometry
 The geometry for refraction
follow the same rules as
reflection.
• Normal to the surface
• Incident angle qi
• Reflected angle qr
 There is also a refracted ray.
• Transmitted angle qt
Snell’s Law
sin q i i

sin q t t
i nt

t ni
ni sin qi  nt sin qt
 The ratio of the sines of the
incident and reflected angles is
proportional to the relative
wavelengths in the material.
 The wavelength is inversely
proportional to the index.
 Combined they become Snell’s
law of refraction.
Bending In
 Light is refracted into a crown
glass slab at 30.0°. Find the
angle in crown glass.
• n1 = 1.00 and n2 = 1.52
• θ2 = sin-1(n1 / n2) sin θ1 = 19.2o
 The ray bends toward the
normal.
• Always true for the higher
index of refraction
Bent Rays
 The refraction at the interface
between water and air can
cause objects to appear in the
wrong place.
 A split spoon in a clear glass of
water is a common example.
Mirage
 Air temperature affects the index of refraction.
• Lower for less dense, hot air
 The difference causes refraction.
Inversion
 At some times of the year there is a layer of cool air near
the ground.
• Inverted mirage
Prism
 The index of refraction
depends on the wavelength.
• Longer wavelengths - lower
indexes
 A triangular prism has two
refracting surfaces.
• One into glass
• One back to air
 The wavelengths are
separated into a spectrum.
Polarization
 At an interface light becomes
partially polarized.
• Separated beams reflected
and transmitted
 If the beams are perpendicular
then the reflected ray is fully
polarized.
q B  qi  q r  90  qt
nt sin( 90  q B )  ni sin q B
nt
tan q B 
ni
• Brewster’s angle
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