1. Goal: To understand the basics of reflection and refraction Objectives: 1)To understand the Propagation of light 2)To understand the following possibilities When light hits something: Reflection Refraction Critical Angle Brewster’s Angle 3) To learn about Rainbows

2. 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?

3. 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 1/4 th the energy (translation – you get cold).

4. 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 hitting) The % of light that gets reflected depends on the material it is hitting as well as the wavelength of light.

5. 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.

6. 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).

7. 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.

8. 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

9. Snell’s Law This accordion affect will change the angle the transmitted light is going (remember you can have some reflected AND some transmitted). n1 sin(θ1) = n2 sin(θ2)

10. 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

11. 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)?

12. 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 degrees. Why would this be important?

13. Sample For our example of light going from a diamond (n=2.4) to ice (n=1.3) what is the critical angle?

14. Brewster’s 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 Brewster’s angle.

15. Equation 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 angle?

16. 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.