1 Refraction, the Snell law Light in geometric optics is discussed in rays and represented by a straight line with an arrow indicating the propagation direction. Light propagates in straight lines in homogenous medium. Light reflects on interface of two media, following the law of reflection: Light also refracts on the interface of two media, following Snell’s law of refraction: Incident light Normal of the interface Reflected light θ 1 and θ 2 are both with respect to the normal of the interface. The parameters n 1 and n 2 are call the index of medium 1 and 2 respectively. Medium 1 Medium 2 θ1θ1 θ2θ2

2 Refraction, the index of refraction of a medium Light travels with the speed of light c in vacuum with c = 3.00×10 8 m/sec. Light travels with a speed v in a transparent medium with v is always smaller than the c. The ratio of c to v is called the index of the refraction n of that medium and is weak function the light frequency. We will get to the frequency dependence part later. And it is this light speed difference in two different media that makes light a turn at the interface of the two media. Have you ever driven a tractor on belts or a tank? You turn to the direction by slowing that side of the belt down. So light travels almost at the speed of light c in air. But light moves in diamond at about 40% of the speed of light c in vacuum. This is why diamond is so pricey. (you believe me here?)

3 Snell’s Law examples θ1θ1 θ2θ2 If θ 1 is 60 degrees, what is θ 2 ? air 1 water 2 θ1θ1 θ2θ2 If θ 2 is 35 degrees, what is θ 1 ?

4 Snell’s Law examples θ1θ1 θ2θ2 θ3θ3 If θ 1 is 40 degrees, what is θ 2 and θ 3 ?

5 total internal reflection θ1θ1 θ2θ2 θ3θ3 air 1 water 2 θ2θ2 θ1θ1 When θ 2 is 30 degrees, θ 1 is 41.7 degrees. When θ 2 is 40 degrees, θ 1 is 58.7 degrees. When θ 2 is degrees, θ 1 is 90 degrees. When θ 2 is 60 degrees, this is a refection problem. So θ 2 is degree, comes from Is called the critical angle θ c. Beyond it, total internal reflection happens.

6 Total internal reflection Total internal reflection only happens when light travels from a medium with larger index of refraction to a medium with smaller index of refraction. The critical angle θ c calculated below. Beyond it, total internal reflection happens. Example: light travel from glass to air, what is the critical angle when total internal reflection happens?

7 Example You are cutting a sapphire to make it as brilliant as possible. Find the critical angle for the sapphire in air. The index of refraction of a sapphire is What would be the cut angle for diamond? And for glass?

8 Fiber optics What is the maximum angle α that results in total internal reflection inside the fiber optic cable? This angle is usually called the launching angle in fiber optics.

9 Wavelength of light in different media Color is often associated with wavelength. It is actually defined by the electromagnetic wave’s frequency. In vacuum, these two values are connected with the speed of light c in vacuum. When light travels in a medium with index of refraction n, the color and frequency keeps the same. Its wavelength changes as: Frequency wavelength so, becomes shorter

10 Wavelength of light in different media Can you prove:

11 Dispersion and prisms The index of refraction is a weak function of wavelength that causes light to separate into its various wavelengths when it is refracted. This is the physics base for the rainbow. Each rain drop Question: if the incoming light is from a red laser, what color(s) do you see when the light exits the prism?