Re: Why are parabolic mirrors used in things such as car headlights?

Well, to start, parabolic mirrors are concave. So you are almost answering your own question.

Perhaps you meant to ask, "Why parabolic mirrors instead of spherical mirrors?" It certainly is easier to manufacture a spherical surface than a parabolic one. So why spend all the extra effort to make a parabolic mirror?

The answer is not too complicated: parabolic mirrors work better to produce nice, tight beams of light. It will be easier to explain if we turn the process backwards for just a moment, and consider what happens when a nice beam of light strikes a mirror.

If the mirror is flat, then the beam just bounces off and continues in a straight line. The beam retains the same width and shape it had before it struck the mirror.

But if beam of parallel light rays strikes a parabolic mirror, something very special happens. The light rays near the outer edges of the beam hit the mirror at some gentle angle, which directs them in a new direction. The light rays near the center of the beam strike the mirror more directly, and are thus reflected in a slightly different direction. However, it turns out that the slightly different directions given to the light rays in different portions of the beam cause them to all converge to a single spot: the focus of the mirror. You can see some nice diagrams showing this property of parabolic mirrors -- and some examples of people using them to cook food! -- at

http://www.humboldt.edu/~ccat/solarcooking/parabolic/parabolic_solar_cooker_pg_3_html.htm

A nice little applet which shows this effect can be found at

http://www.cut-the-knot.org/Curriculum/Geometry/ParabolaMirror.shtml

If a similar beam of parallel light rays strikes a spherical mirror, the light beams are reflected at angles that cause them to head towards each other; but they don't quite meet at a single point. Instead, the light rays pass each other over a range of positions. The rays will never come together as completely as they will when reflected by a parabolic mirror. This failure of spherical mirrors to create a perfect focus is called spherical aberration. You can read a longer description of this effect in the Physics Classroom:

http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l3g.html

Right. Now, back to your question.

A car's headlight is supposed to take the light emitted by a bright lamp and throw it forward so that it illuminates the road as far ahead as possible. If the beam produced by the headlight spreads out quickly, very little light will strike the road -- and obstacles -- which lie far ahead of the car. So the headlight should make a beam of light rays which are all bunched together, pointing in the same direction: straight ahead.

Lamps, unfortunately, don't do that. The hot metal filament in a lamp produces light rays which fly outwards in all directions. Some of them will go straight ahead, but the rest will be wasted unless we can somehow redirect them.

What we want to do is take these diverging light rays which are created in a small region (the lamp) and reflect them at different angles so that they end up pointing parallel to each other. This is exactly what I described above, except in reverse: there, we wanted to turn a beam of parallel light rays into a converging beam that came together at a point (the focus). So, if we place the lamp at the special focus point of a parabolic mirror, the light rays it produces will bounce off the mirror and shoot outwards in a parallel beam down the road. That parallel beam of rays will illuminate distant objects most clearly.