Goal: To understand the basics of reflection and refraction

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Goal To understand the basics of reflection and
refraction

• Objectives
• To understand the Propagation of light
• To understand the following possibilities When
  light hits something
• Reflection
• Refraction
• Critical Angle
• Brewsters Angle
• 3) To learn about Rainbows

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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 back?

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Spreading of light

• Since light propagates in all 3 dimensions that
  means it spreads itself out onto the surface of a
  sphere.
• 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).

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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 (?r ?i), as is the
  wavelength of light (in the perspective of the
  object it is hitting)
• The of light that gets reflected depends on the
  material it is hitting as well as the wavelength
  of light.

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Transmitted

• 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.

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Absorption

• 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
  energy.
• Thus water vapor is a greenhouse gas (and the
  most abundant greenhouse gas in our atmosphere).

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Scattering

• 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 surface.
• 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.

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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, ect.
• 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

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Snells Law

• This accordion affect will change the angle the
  transmitted light is going (remember you can have
  some reflected AND some transmitted).
• n1 sin(?1) n2 sin(?2)

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Sample

• 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

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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 (n1.3).
• What is the angle of refraction (yes you will get
  a really wild answer no your calculator is not
  malfunctioning)?

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Critical Angle

• The most Sin(?) 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(?2) 1
• (in other words Sin(?1) n2 /n1)
• Here ?1 (or ?c) 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 degrees.
• Why would this be important?

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Sample

• For our example of light going from a diamond
  (n2.4) to ice (n1.3) what is the critical angle?

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Brewsters angle

• Another way to polarize light is through
  reflection.
• The fraction which is polarized depends on the
  reflecting surface and the angle.
• At a specific angle all of the light is
  polarized.
• This is called Brewsters angle.

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Equation

• tan(?b) n2 / n1
• In this case it does not matter which is bigger
  you still have an angle.
• Sample For the diamond (n2.4) to ice (n1.3)
  example, what is Brewsters angle?

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Conclusion

• 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.