Dispersion
There is one subtlety of refraction that we’ve overlooked: the index of refraction depends
slightly on the wavelength of the incident light. When a mixture of waves of different
wavelength refract, each constituent color refracts differently—the different constituents
disperse. Generally speaking, light of a longer wavelength and lower frequency refracts
less than light of a shorter wavelength and higher frequency, so.
The phenomenon of dispersion explains why we see a rainbow when sunlight refracts off
water droplets in the air. The white light of the sun is actually a mixture of a multitude of
different wavelengths. When this white light passes through water droplets in the air, the
different wavelengths of light are refracted differently. The violet light is refracted at a
steeper angle than the red light, so the violet light that reaches our eyes appears to be
coming from higher in the sky than the red light, even though they both come from the
same ray of sunlight. Because each color of light is refracted at a slightly different angle,
these colors arrange themselves, one on top of the other, in the sky.
We find the same phenomenon with light shone into a glass prism.
Optical Instruments
The reflection and refraction we’ve dealt with so far have focused only on light interacting
with flat surfaces. Lenses and curved mirrors are optical instruments designed to focus
light in predictable ways. While light striking a curved surface is more complicated than
the flat surfaces we’ve looked at already, the principle is the same. Any given light ray
only strikes an infinitesimally small portion of the lens or mirror, and this small portion
taken by itself is roughly flat. As a result, we can still think of the normal as the line
perpendicular to the tangent plane.