Reflection
The first property of light we consider is reflection from a surface, such as that of a mirror.
This is illustrated below.
Law of reflection
When light is reflected off any surface, the angle of incidence θ1is always equal to the
angle of reflection θ2.
Note:


The angles are always measured with respect to the normal to the surface.
The law of reflection is also consistent with the particle picture of light.
Refraction
Definition: Refraction
Refraction is the bending of light as it passes between materials of different optical
density.
Definition: Index of Refraction
Index of Refraction of a material is the ratio of the speed of light in vacuum to the speed
of light in that material:
c
(1)
n= v
where v is the speed of light in the material.
Note:


The more dense the material, the slower the speed of light in that material. Thus n > 1
for all materials, and increases with increasing density. n = 1 in vacuum.
The frequency of light does not change when it passes from one medium to another.
According to the formula v = λ f , the wavelength must change. The index of refraction
can therefore be written in terms of wavelengths as:
n=

(2)
where λo is the wavelength of the light in the vacuum and λ is the wavelength of the
light in the medium.
Idea: Explanation for Refraction of Light
The change in speed and wavelength at the boundary between two materials causes light
to change direction. Think of a car approaching a patch of mud at a sharp angle from a
well paved road. The tyre that hits the mud first will slow down, while the other tyre is still
going fast on the good road. This will cause the car to turn, until both tyres are in the mud
and going at the same speed. If θ1 is the angle of the ray relative to the normal to the
surface in medium 1, and θ2 is the angle relative to the normal in medium 2, then:
=
=
=
where v1 and λ1 are the speed and wavelength in medium 1, etc.
This is illustrated below.
Law of refraction
λ1
Note:


This relationship between the angles is called Snell's Law.
The relation between the two angles is the same whether the ray is moving from
medium 1 to 2 (so that θ1 is the angle of incidence and θ2is the angle of refraction) or
whether the ray moves from medium 2 to medium 1, so that θ2 is the angle of
incidence and θ1 is the angle of refraction.
Total Internal Reflection
For a light ray passing from a more dense to a less dense material, there is a critical angle
of incidence θc for which the angle of refraction is 90 o. For greater angles of incidence, the
light cannot pass through the boundary between the materials, and is reflected within the
more dense material. For a light ray trying to pass from medium 2 to medium 1, the
critical angle is given by:
sin θc =
where n1 is the index of refraction of the less dense material, and n2 is the index of
refraction of the more dense material.
Note: The formula for the critical angle shows that n2 must be greater than n1 for there to
be total internal reflection. That is, medium 2 must be more dense than medium 1.
Otherwise sin θc > 1, which is not possible.
Material
Index of Refraction
Vacuum
1.0000
Air
1.0003
Ice
1.31
Water
1.333
Ethyl Alcohol
1.36
Plexiglas
1.51
Crown Glass
1.52
Light Flint Glass
1.58
Dense Flint Glass
1.66
Zircon
1.923
Diamond
2.417
Diffraction
Diffraction is the apparent ``bending'' of light waves around obstacles in its path.
Diffraction of
waves through a
slit
This bending is due to Huygen's principle, which states that all points along a wave front
act as if they were point sources. Thus, when a wave comes against a barrier with a small
opening, all but one of the effective point sources are blocked, and the light coming
through the opening behaves as a single point source, so that the light emerges in all
directions, instead of just passing straight through the slit.
Note:


For sizeable diffraction effects to occur the width of the opening must be of the same
order or less than the wavelength of the light used.
Diffraction limits the resolving power of microscopes and other magnifying devices. If
the object being viewed is smaller than the wavelength of light used, then the light
diffracts around the object, and severely distorts the image. Thus microscopes using
visible light have a resolving power of only about 600 nm 10- 6m, but X-rays, whose
wavelength is about 0.1 nm ( 10- 10 m) have a resolving power four orders of
magnitude smaller.
Interference
Definitions

Two waves (of the same wavelength)
are said to be in phase if the crests (and
troughs) of one wave coincide with the
crests (and troughs) of the other, as in
the figure below.
Constructive Interference
In this case the resultant wave would have twice the amplitude of the individual waves
- one says that constructive interference has occurred.

If the crest of one wave coincides with the trough of the second they are said to be
completely out of phase,
Destructive Interference
In this case the two waves would cancel
each other out - one says that destructive
interference has occurred. At a point of
constructive interference the net
amplitude of the two waves is a maximum,
whereas at a point of destructive
interference, the net amplitude is a
minimum. Of course, one could also have
situations in between these two extremes.
Idea: If two identical waves of wavelength λ start out in phase, travel at the same speed
for a distance of r1 and r2 respectively, where r1 > r2 , the crests of the one wave will be
behind the crests of the other by a distance of r1 - r2 . The condition for constructive
interference when the waves recombine is
r1 - r2 = mλ , m = 1,2,....
The condition for destructive interference is
r1 - r2 = (m + )λ , m = 1,2,...