## 20120117

### Presentation: redirecting light

Now that we've already been introduced to "light," that is, the electromagnetic spectrum, let's take a look at redirecting (visible) light. Note that like presentations in the previous first semester of this college physics sequence, this presentation will hopefully give you a sense of what Bill Nye ("The Science Guy") likes to describe as "PBJ"--the "passion, beauty, and joy" of reflecting and refracting light. We simply don't have time for an exhaustive, comprehensive discussion of this material in class--that's what your textbook is for!

Reflection is redirecting light by bouncing it off of a surface.

Conventionally we consider reflections off of flat surfaces. (Don't worry about what's about to happen here--it's art!)

Even with reflections off of curved surfaces, each point on it can be considered a locally flat surface.

And more "PBJ" for reflections--they have the curious property of reversing front-to-back symmetry (or here in this perspective, left-to-right symmetry).

The law of reflection is simple geometry--for a (visible) ray of light incident on a flat surface, if we measure the angle of incident with respect to the normal (a line drawn perpendicular to the surface), the reflected ray will make the same angle as it leaves the surface. (This law also applies for curved surfaces, provided we look close enough such that it look locally flat.)

Instead of bouncing light off of surfaces, if light can pass into a transparent material, we will have refraction, where it is redirected by being "bent."

Refraction occurs when light starts in one material, and passes into another. (This art installation only gives the illusion of seeing light from people underwater; instead there is only a thin layer of water supported by sheet of glass between these two levels.)

When light does start in one medium, and pass into another medium, it will refract, or bend, which can produce curious results.

Look at the exhaust plume from this jet: heat warms the air and changes its density, making light travel at a different speed through it, and it will be bent in interesting directions. Also note the shockwaves from leading edges on the jet--here air is compressed, and again light traveling through it will be bend it in interesting directions.

Now take a look at this transparent block. Light will travel with a different speed through it than through air, and so the light will be bend in interesting directions. Why can't we see the block when we pour water around it? (Video link: "100108-1140566.")

Quantitatively, "Snell's law" describes how light will bend as it passes from one medium into another medium. Note that angles for both the incident ray and refracted ray are measured with respect to the normal (that imaginary line drawn perpendicular to the interface between the two media). The medium with the lower index of refraction will have the larger angle (actually, the larger sine of that angle). (This law of refraction is commonly known as "Snell's law," but in France it is referred to as "Descartes' law," as René Descartes was French, while Willbrord Snellius was Dutch.)

Since the index of refraction is a measure of the "optical slowness" of a material, a faster speed of light corresponds to a lower index of refraction, and a larger angle, as it travels into a material with a slower speed, a higher index of refraction, and a smaller angle. Mnemonic: "Fast-to-slow, bend towards the normal."

Consider starting in a medium with a greater index of refraction. Note that angles for both the incident ray and refracted ray are still measured with respect to the normal (that imaginary line drawn perpendicular to the interface between the two media). The medium with the higher index of refraction will have the smaller angle (actually, the smaller sine of that angle).

And since the index of refraction is a measure of the "optical slowness" of a material, a slower speed of light corresponds to a higher index of refraction, and a smaller angle, as it travels into a material with a faster speed, a lower index of refraction, and a larger angle. Mnemonic: "Slow-to-fast, bend away from the normal."