Reflection and Refraction

REFLECTION

You may recall from class the simple, elegant Law of Reflection:

angle of incidence equals angle of reflection.

Think about pool balls hitting the side of a billiards table - angle in equals angle out.

The only tricky part is the way we measure angles - they are measured with respect to a "normal line", a line that is perpendicular to the surface where they hit.


REFRACTION

Refraction refers to a wave changing mediums - going from air to glass, air to water, water to air, glass to air, etc. We first begin by defining a new quantity, the index of refraction (n):

n = c/v

where c is the speed of light and v is the speed of light in the NEW medium. Indices of refraction are always greater than (or approximately equal to) one, and have NO units.

For example, if a substance (say, glass) slows down light to 2/3 of the speed of light (in a vacuum), its index is:

n = c/(2/3 c) = 1.5

A convenient relationship can be derived that relates the angle of incidence and the angle of refraction, along with the indices of refraction of the two mediums. It is called Snell's Law:

n1 sin(theta 1) = n2 sin(theta 2)

As before, the angles are measured with respect to a normal (perpendicular) line. It may be helpful to remember:

- When light goes from a lower density medium (n1) to a higher density medium (n2 > n1), the light ray is refracted TOWARD the normal line. And vice versa.


CRITICAL ANGLE

There is an angle, above which light can not leave the medium. Imagine a light ray trying to go from water into air. Clearly, the light ray will refract AWAY from the normal line. If you gradually increase the angle of incidence (theta 1), eventually the refracted angle (theta 2) will become 90 degrees - light "skating" across the surface.

Any theta 1 greater than this angle will result in "total internal reflection", wherein the light simply cannot leave the substance - it is reflected back inside the original medium. This is the secret of fiber optics. The mathematics come from Snell's Law:

n1 sin(theta 1) = n2 sin(90)

n1 sin(critical angle, ic) = 1 (1)

sin ic = 1/n

That is, the sine of the critical angle equals 1 over the index of refraction for that particular medium (assuming that medium 2 is air, so that n2 = 1).

Got it? Good!