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Goal: To understand the basics
of reflection and refraction
1) To understand the Propagation of light
2) To understand the following possibilities
When light hits something:
Critical Angle
Brewster’s Angle
3) To learn about Rainbows
Propagation of light
• When light is emitted – even a single
photon – it usually goes in all directions.
• Imagine you are camping on a cold day.
• You start a fire to warm yourself.
• What happens if you take a few steps
Spreading of light
• Since light propagates in all 3 dimensions that
means it spreads itself out onto the surface of a
• Since the area of the outside of this sphere (not
volume) relates to the radius squared that
means that the light you receive – or energy –
drops as the radius squared.
• So, if you get twice as far away you only get
1/4th the energy (translation – you get cold).
When a photon meets a woman,
err a surface
• A few things can happen, and often times you
will get all of these in different amounts.
• 1) reflection – the light in essence bounces off of
the surface.
• In this case the angle which the light leaves is
the same as it hits (θr = θi), as is the wavelength
of light (in the perspective of the object it is
• The % of light that gets reflected depends on the
material it is hitting as well as the wavelength of
• 2) Some light will be transmitted. That is it
will pass through the material.
• This will also cause what is called
refraction – but more on that later.
• 3) The material can absorb some of the energy.
• The percentage it absorbs at some wavelength
is called the albedo.
• This can vary greatly with wavelength.
• A thin layer of water, for example, does not
absorb much light in the optical.
• However, in the infrared it absorbs a LOT of
• Thus water vapor is a greenhouse gas (and the
most abundant greenhouse gas in our
4) Scattering.
This is similar to reflection.
However, most surfaces are not smooth.
So, when the light hits the surface, it is not hitting a flat
• So, different light photons at slightly different positions
can hit at a vastly different angle to the surface.
• Therefore, they will reflect at a wide range of angles.
• This is scattering.
• Also, if light hits an electron the electron can absorb the
photon and reemit in a random direction – thus
scattering the light.
More on Refraction
• A surface is defined to be a point where the index of
refraction changes.
• The most common form of this is when you have 2
different types of materials – such as air, glass, water,
• For each the speed of light is different.
• When the light enters the material the speed changes
but the rest of the wave which has not hit the surface is
still going at the old pace.
• This causes an accordion affect (like cyclists hitting a hill
and piling up).
• Also, the index of refraction depends on the wavelength
of light – more on this at the end of class
Snell’s Law
• This accordion affect will change the angle
the transmitted light is going (remember
you can have some reflected AND some
• n1 sin(θ1) = n2 sin(θ2)
• On a winter day the light from the sun hits
a clear calm lake at an angle of 60
degrees from normal (up and down).
• If the index of refraction of the water is 1.4
then what are:
• A) the angle of reflection
• B) the angle of refraction
Try one more
• Lets say a beam of light traveling at an
angle of 75 degrees from normal in a
diamond (n =2.4) enters into ice (n=1.3).
• What is the angle of refraction (yes you
will get a really wild answer – no your
calculator is not malfunctioning)?
Critical Angle
• The most Sin(θ) can be is 1
• That means that if you go from high index of
refraction to low index of refraction there is a
point where Sin(θ2) = 1
• (in other words Sin(θ1) = n2 /n1)
• Here θ1 (or θc) is called the Critical Angle.
• If your initial angle is BIGGER than this, then
there is NO refraction (this is called total
internal reflection)!
• At the critical angle the angle of refraction is 90
• Why would this be important?
• For our example of light going from a
diamond (n=2.4) to ice (n=1.3) what is the
critical angle?
Brewster’s angle
• Another way to polarize light is through
• The fraction which is polarized depends on
the reflecting surface and the angle.
• At a specific angle all of the light is
• This is called Brewster’s angle.
• tan(θb) = n2 / n1
• In this case it does not matter which is
bigger you still have an angle.
• Sample: For the diamond (n=2.4) to ice
(n=1.3) example, what is Brewster’s
• We learned what can happen when light hits a
spot where the index of refraction changes.
• Reflecting light goes at the same angle it hits
(from point of view of the surface)
• Refracted light will depend on the difference of
mediums and the angle.
• At some angle (critical angle) the refracted angle
is 90 degrees – so you get no refraction bigger
entry angles.
• Also, reflections polarize light and at a special
angle, the Brewster angle, all the reflected light
is polarized.