1. October 15 – outline: What we did last time – “memory refresher”: “Pedroni“Pedroni”, Page 8, laws of light reflection. Next, start taking about refraction of light: “Pedroni”, pages 10-11 (basic facts). Then, continue with this PPT presentation.

2. Basic facts: light incident on a water or glass surface, is partially reflected, and partially refracted: Refraction may produce spectacular Visual effects: Explanation why objects in water seem to be closer to the water surface than they actually are – which causes the “broken stick” effect.

3. More about refraction, and total internal reflection Vacuum Medium * If we only say “refractive index”, it by default means “relative to vacuum”.

4. If the ray impinges on the surface from vacuum, the angle of incidence, the angle of refraction, and the refractive index satisfy the relation: This is known as the Snell’s Law. If there are two different media, as shown in the figure, then the Snell’s Law has the form: Note that it is consistent with the upper one. Suppose that Medium 1 is vacuum; and, obviously: So we indeed get the same formula as the “upper” one.

5. Here is an animated example. A ray is incident from air on water surface. The refractive index of air is 1.0003, so with a good approximation can be taken as 1. For water, it is easy to remember: n = 4/3 = 1.3333. We change the angle of incidence from 0 to 90º. The angle of refraction is always smaller. What is its maximum value?

6. Now we want to consider, what happens, if light impinges on the water surface, but “from below”. Here The Principle of Ray Reversibility comes in handy: Any actual ray of light in an optical system, if reversed in direction, will retrace the same path backward

7. The maximum value sin(θ r ) can take is 1. It happens when sin(θ i ) = ¾ = 0.75, it is, when θ i = 48.59º θ i = 48.59º in the present case is the critical angle. For θ i larger than the cri- tical angle the Snell Law is no longer valid! For θ i > 48.59º, light inci- dent “from below” on wa- ter surface is no longer refracted, but totally ref- lected – this effect is called a total internal reflection of light.

8. Here is the same animation, but a slower one:

9. Let’s discuss: a diver underwater looks up – what does she see?