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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 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? 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). 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. 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. 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). 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. 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 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) 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 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 degrees. • Why would this be important? Sample • 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 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. 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? 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.

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