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The Nature of Light
• The earliest (~1000 A.D.) description of light was
that of a stream of tiny particles
– Newton described light with a particle model as well
• Huygens described many properties of light
successfully using a wave picture (1670)
• Young showed that light beams can interfere with
one another (1801), giving strong support to wave
theory
• Maxwell’s theory of electromagnetic waves included
light (1865)
• Results of early 20th Century physics experiments
could only be explained using a particle picture of
light
The Nature of Light
• Einstein explained the results of the photoelectric
effect experiment using the concept of photons
(1905)
– The energy E of a photon is proportional to the frequency
f of the electromagnetic wave
• h = Planck’s constant (a very small number)
E  hf
• So what is light, a wave or a particle?
• Experiments show that it must be both!
– But never both at the same time
– A “wave-like” experiment will give wave-like results
– A “particle-like” experiment will give particle-like results
The Ray Approximation
• Light travels in a straight-line path in a homogenous
medium until it encounters a boundary between two
different materials
• Thus light propagation can be approximated as rays
drawn along the direction of travel of the light beam
– Rays are perpendicular to the
wave fronts
– Wave fronts are nearly planar
for light that is far from its
source (“plane waves”)
Reflection
• When light reaches a boundary between 2 media,
some of the light is reflected back into the incident
media
Specular reflection (smooth surface) Diffuse reflection (rough surface)
• For specular reflection:
1  1
(Law of Reflection)
Refraction
• When light reaches a boundary
between 2 transparent media,
some of the light is reflected back
and some is refracted (bent) into
the other media
– Angle of refraction = 2
sin  2 v2
  constant
sin 1 v1
– Light is bent either toward
or away from the normal,
depending on its relative
speed in each medium
Refraction
• Think of a barrel rolling toward
the interface between two
unlike surfaces
• Refraction is responsible for
being able to see objects that
would otherwise be outside
your field of view
Law of Refraction
• It is convenient to define an index of refraction, a
constant, unitless number for a particular medium
speed of light in vacuum c
n

speed of light in a medium v
• As light travels from one medium to another, its
frequency does not change
– Otherwise waves would “bunch up”
or be created or destroyed at
boundaries between different media
– Since v = f l, wavelengths must
change at boundaries
– Thus we have: v1 = f l1 and v2 = f l2
– Also: l1n1 = l2n2
Law of Refraction
• Thus wavelength of light
gets smaller (larger) when
it enters medium of
larger (smaller) n
• Snell’s law of refraction:
n1 sin 1  n2 sin 2
– Light refracts toward
(away from) normal when
n1 < n2 (n1 > n2)
– 1, 2 are measured
with respect to the
normal
n1 = 1.00
n2 = 1.52
n1 = 1.52
n2 = 1.00
Example Problem #22.19
When the light ray
passes through the
glass block as shown, it
is shifted laterally by a
distance d. Find the
value of d.
Solution (details given in class):
0.388 cm
Transmission Through 3 Media
Example Problem #22.28
A cylindrical cistern, constructed below ground
level, is 3.0 m in diameter and 2.0 m deep and
is filled to the brim with a liquid whose index of
refraction is 1.5. A small object rests on the
bottom of the cistern at its center. How far
from the edge of the cistern can a girl whose
eyes are 1.2 m from the ground stand and still
see the object?
Solution (details given in class):
2.5 m
Applications of Reflection and Refraction
• The index of refraction depends on
wavelength (dispersion)
• Thus the angle of refraction when light
enters a material depends on its
wavelength
– Violet (l ~ 400 nm) deviates the most
– Red (l ~ 650 nm) deviates the least
– Principle behind the prism and formation
of rainbows
Max. angles 
Rainbows
The Raindrop
Rainbows
http://www.unidata.ucar.edu/staff/blyndds/rnbw.html
Total Internal Reflection
• When light attempts to move from a medium with a
higher index of refraction to one with a lower index of
refraction, total internal reflection can occur
– At some critical angle c the refracted light ray
moves parallel to the boundary
– When 1 = c , 2 = 90° and Snell’s
law gives:
n2
sin  c 
o
n1 sin c  n2 sin 90  n2
n1
for n1  n2
Application: Fiber Optic Cables
• Example of total internal reflection within solid glass
or transparent plastic rods
– Used to “pipe” light from one place to another with very
little loss of light intensity
– Used frequently by doctors as an imaging tool
(N1 > N2)
– Light can travel through bends or light
“kinks” in rod without losses
Example Problem #22.47
The figure above shows the path of a beam of light through several layers with
different indices of refraction. (a) If 1 = 30.0°, what is the angle 2 of the
emerging beam? (b) What must the incident angle 1 be in order to have total
internal reflection at the surface between the medium with n = 1.20 and the
medium with n = 1.00?
Solution (details given in class):
(a) 53.1°
(b) 38.7°
Interactive Example Problem:
Snell’s Law and Total Internal Reflection
Animation and solution details given in class.
(PHYSLET Physics Exploration 34.2, copyright Pearson Prentice Hall, 2004)