Everyday Optics: Rearview Mirrors

I have been helping some friends study for the qualifying exam lately, and part of that has been coming up with problems for them to ponder and answer. As I've done this, I've realized just how much optical phenomena surround us everyday, and just how much of it can be treated in terms of simple geometrical optics. (Why I didn't discover this when I myself was studying is anyone's guess).

Take, for example, your rearview mirror. If you drive, you know this mirror is a good friend. And if you do a lot of night driving, you know that moving that little lever on the bottom forward means you don't have to be blinded by the headlights of the guy behind you. But you probably have not thought about why that works. You are just thankful it does when the idiot behind you has his brights on. 

The way that this works is simple, cool and demonstrates the usefulness of basic optics.

First, let's look at the case of the normal, daytime mirror. In this situation, it works like any other mirror. You have a piece of silvered glass (glass with a highly reflective material on one side) that is angled so that it directed light from objects directly behind the driver's right shoulder into the driver's eyes. 

Yes, I do illustrations on my whiteboard.

From an optical standpoint, there are two reflective surfaces or interfaces. Reflections occur wherever there is an index mismatch, and the stronger the mismatch, the stronger the reflection. How much reflection occurs can be found using the Fresnel Equations.  In the case of a rearview mirror, we have a air/glass and a glass/reflective coating interface. One other thing to note is that rearview mirrors are not like your bathroom mirror, which is made of planar glass. Rather, rearview mirrors are prismatic, which is to say if you cut one in half from top to bottom, you would notice that the glass is ever so slightly trapezoidal, like this:

This allows you to choose which reflection you want to use--the silvered surface reflection for daytime driving, where everything is the same brightness, thanks to sunlight.

Or the first glass surface at night, where you just want enough light to know someone is behind you, because you aren't going to get any kind of detail from the reflected image anyway. Notice that the light still is reflecting off the silvered surface, but now it is being reflected at the ceiling. In fact, if you accidentally leave it in the night position during the day, you'll notice a very faint reflection of what's behind you, and a much stronger reflection of your car ceiling.

Behold! PhysicsGal in her minivan, parked safely in her garage.

Alright, I admit it. Geometrical optics is kinda cool and useful. Only took me...6 years to figure that out? I think I'm ashamed of myself.