GEO - Refraction and Snell's Law

Refraction and Snell's Law

Index of Refraction

The speed of light in a vacuum, c is considered a constant and has a value of 3.00 x 10⁸m/s. However, when light travels through a medium, the speed decreases. The ratio of the constant speed of light in a vacuum to the speed in a given medium is known as the index of refraction. The equation is:

Here n is the index of refraction, c is the speed of light in a vacuum, and v is the speed of light in the given medium. Since the index is a ratio of speeds, it is a unitless value. Also, since the speed of light in a vacuum is the maximum possible speed, the index of refraction for any medium must have a value of one or greater.

This table lists the indices of refraction for many common mediums (for light of wavelength 589nm)

Medium	n = c/v
Vacuum	1.0000
Air (@ STP)	1.0003
Water	1.33
Ethyl alcohol	1.36
Quartz glass	1.46
Crown glass	1.52
Flint glass	1.58
Lucite (Plexiglass)	1.51
Sodium chloride	1.53
Diamond	2.42

A few of points of interest from this chart:

• Light slows only slightly when passing through air. To only three significant figures, the index of refraction for air = 1.00. You should memorize this value. It will be used often.
• Another index of refraction you should memorize is n water = 1.33.
• Having an index of refraction of greater than two shows that light speed is more than cut in half when passing from vacuum/air into diamond.

You can think of the index of refraction equation as a conversion equation. With it you can convert from speed to index of refraction or index of refraction to speed.

Refraction and Snell's Law

When light passes into a new medium with a different index of refraction, its path changes. This change in path is called refraction.

In this image a light ray is shown striking the boundary between air and water. For the light that is transmitted into the water, its speed decreases and its path direction is changed. If you've ever looked at a straw in a clear glass of liquid, you may have noticed how it can appear to be bent or separated, depending on what angle you observe it from. This is a result of the light waves from the straw refracting as they leave the water in the glass and eventually pass into the air.

In our refraction ray diagram you can see how the angle of incidence, θ₁ can be measured between the normal and the incident ray in medium 1 (air). The angle of refraction, θ₂ is shown as being measured between the refracted ray and the normal in medium 2 (water).

Willebrord Snell is credited with determining that the relationship between the angle of incidence and the angle of refraction is based on the relative speed of light in each medium. This relationship is known as Snell's law:

The following relationships can be determined using Snell's law:

• For n₂ > n₁ (light slows down in medium 2), θ₂ < θ₁ (light path bends towards the normal)
• For n₂ < n₁ (light speeds up in medium 2), θ₂ > θ₁ (light path bends away from the normal)

The classic example of light refracting towards the normal is when light passes from air into water. If the light were to go from water into air, however, the refraction would cause the ray to be bent away from the normal.

Total Internal Reflection

We've seen that light traveling from a fast medium to a slower medium will refract towards the normal. If light travels in the opposite direction, from a slow to a faster medium, it is refracted away from the normal. At some critical angle the light refracts at 90 degrees. At any angle of incidence greater than the critical angle the light reflects off the boundary and stays within the incident medium. This phenomenon is known as total internal reflection. 

Dispersion

So far we've focused our discussion of refraction on what happens to light of a specific wavelength. Our table above listing the index of refraction for different media is based on light with a wavelength of 589 nm. This is because the index of refraction for a medium is different at different wavelengths. Isaac Newton, in his investigation of light, showed that shining white light through a prism broke the light up into its constituent colors, the colors of visible light. This phenomena, known as dispersion, occurs because the differences in indices of refraction for each wavelength results in a different angle of refraction. Light at the violet end of the visible spectrum is refracted most while light at the red end is refracted least.

The dispersion of sunlight through rain drops causes the appearance of rainbows after a storm. As light enters the top front of the rain drop it begins to be dispersed through refraction. If the light strikes the rain drop at the correct angle, the refracted light will strike the back of the raindrop at an angle equal to or greater than the critical angle for water and air. The reflected light refracts again as it leaves the bottom front of the drop, increasing the angle between the red and violet wavelengths. Since red light is sent more downward, you see it first, making up the upper band of the rainbow. As you look down the next band you see is the next set of wavelengths, orange. This continues happening until you see the violet wavelengths at the bottom of the rainbow.

Refraction and Snell's Law Practice

Refraction and Snell's Law Self-Assessment

Click here to access Links to an external site. The Physics Classroom - Refraction Practice.  Work problems: 1 - 4, 7, 8, 13, & 21.

IMAGES AND VIDEOS SOURCED FROM PUBLIC DOMAIN