Goal: To understand light Objectives: 1)To understand how matter affects the speed of light 2)To learn why the Summer is hotter than the winter 3)To learn about Polarization 4)To understand and be able to calculate Doppler effect on light

Speed of light in matter In matter light is slowed. The fraction it is slowed is called the index of refraction (n) n = c / v where v is the velocity of light in that material and c is the speed of light in a vacuum. And good to know that v = λf Quick sample: If the speed of light in a fluid is half the speed of light in a vacuum then what is the index of refraction for that material?

Why are summers hotter than winters?

Polarization A light photon is a 2 dimensional wave (i.e. a wave in a 2 dimensional plane) with some velocity in some direction. Usually each photon will come in at some random plane. This is unpolarized light. However, if the light is emitted preferentially in some plane, or is forced into it, then it will become polarized.

Linear polarization One way to polarize light is linearly. This means that some percentage of light comes in at some specific plane. The % is the % polarization.

Circular polarization If the plane rotates with time in some way it is circularly polarized. However we will not deal with this type of polarization.

Polarizers There are filters called polarizers. These devices absorb all the parts of light not polarized in a specific plane. The parts in the plane get through (sort of like a door for people not paying attention to it).

Light through a polarizer The polarizer has a set angle it wants light to go through. If you shine unpolarized light through it then on average half will line up with it and half will not. So, half the light will get through. I = ½ I 0 Furthermore the transmitted light will be linearly polarized in the direction of the polarizer.

Polarized light through polarizer If polarized light goes through a polarizer then only the parts of the polarized light going in the direction of the polarizer get though. So, I = I 0 cos 2 (θ) Where is the angle between the directions of the polarized light and the polarizer. This is called Malus’s law

Sample Unpolarized light of intensity 5 W/m 2 passes through a polarizer oriented up and down. The light going through the polarizer is then allowed to pass through a 2 nd polarizer which is tilted at a 45 degree angle from up and down. What is the intensity of light entering and leaving the 2 nd polarizer?

Try a harder one… Unpolarized light with intensity of 12 W/m 2 enters a polarizer which is oriented up and down. This light is split in 2. Half goes into a 2 nd polarizer which is oriented 60 degrees from up and down. This light is then sent to a 3 rd polarizer which is oriented 90 degrees from up and down (sideways basically). The other half of the light skips the 2 nd polarizer and goes straight to the 3 rd. What is the intensity of light going into and out of the 3 rd polarizer?

Doppler Effect You have seen this hopefully in P218 (but with sound) The Doppler Effect on light is the same as for sound except that the sound velocity becomes the speed of light. If something is moving then the wavelength of the light emitted will change. If it is moving towards you, wavelength will decrease and frequency will go up. If it is moving away from you, wavelength will increase and frequency will go down.

Equations fobserved = fsource (1 + v/c) Where v is the relative velocity between observer and source. Simple as that. You try a harder one: A cop car moves at 40 m/s to catch up to a car going 10 m/s. The cop car emits a 10 GHz beam at the car. What is the shift in the frequency that the cop car gets back? Hint, you will have to find what the frequency the chased car sees because that will be the reflected frequency.

Conclusion We have learned about the index of refraction when materials slow down light We learned why it is cold in the winter. We learned about polarization and how to calculate fluxes through polarizers. We learned how to calculate the Doppler effect for light.