Refraction of Light Notes

refraction: the change in direction of waves at the boundary between two different mediums

When light encounters a transparent or translucent medium, some light is reflected from the surface, and some is transmitted through the medium.
When light crosses a boundary between two mediums, it bends. This phenomenon is called refraction.

The angle of incidence $\theta_1$ is the angle at which the light ray strikes the surface, measured from the normal to the surface.
The angle of refraction $\theta_2$ is the angle at which the transmitted light leaves the surface, also measured with respect to the normal.
The index of refraction $n$ determines the angle of refraction between two mediums.
Snell’s law of refraction relates the indexes of refraction, the angle of incidence, and the angle of refraction for any two substances.

Problem: A ray of light is incident upon a layer of flint glass ( $n = 1.62$ ) at an angle of $19.0^\circ$ . What is the angle of refraction?
Known:
- $n_1 = 1.00$
- $n_2 = 1.62$
- $\theta_1 = 19.0^\circ$
Unknown:
- $\theta_2 = ?$

If $n<em>2 = 1.00$ (a vacuum), then $v</em>2 = c$ and we see that the index of refraction for a medium is related to the speed of light in the medium.
Index of Refraction: $n = \frac{c}{v}$ , where:
- $n$ is the index of refraction,
- $c$ is the speed of light in a vacuum, and
- $v$ is the speed of light in the medium.

When $n<em>1 > n</em>2$ , the angle of refraction is greater than the angle of incidence.
At a certain angle of incidence, known as the critical angle $\theta_c$ , the refracted light ray lies along the boundary of two mediums.
Total internal refraction occurs when light traveling from a region of higher $n$ to a region of lower $n$ strikes the boundary at an angle greater than the critical angle such that all light reflects back into the region of higher $n$ .
The light traveling through a transparent optical fiber always hits the internal boundary of the optical fiber at an angle greater than the critical angle, so all of the light is reflected and none of the light is transmitted through the boundary.

The speed of light in a substance (and thus the index of refraction) depends on temperature.
Mirages can form when light rays are refracted as they travel through air at different temperatures.
For example, a thermal layering of hot air above the road causes light traveling toward the road to gradually bend upward. This makes the light appear to be coming from a reflection in a pool.
As light from a distant object travels downward toward the road, the index of refraction of the air decreases as the air gets hotter, but the temperature change is gradual.
In the case of a mirage, the Huygens’ wavelets closer to the ground travel faster than those higher up, causing the wavefronts to gradually turn upward.

The speed of light and the index of refraction vary for different wavelengths of light in the same liquid or solid medium.
White light separates into a spectrum of colors when it passes through a glass prism. This phenomenon is called dispersion.
Violet is refracted more than red because the speed of violet light through glass is less than the speed of red light through glass.
Glass has a slightly higher index of refraction for violet light than it has for red light.

A rainbow is a spectrum formed when sunlight is dispersed by water droplets in the atmosphere.
Sunlight that falls on a water droplet is refracted and dispersed.
At the back surface of the droplet, some of the light undergoes internal reflection.
On the way out of the droplet, the light is again refracted and dispersed.