What is Snell's Law?

Victoria Blackburn

In physics, Snell's Law gives the equation that describes how light is refracted when it travels from one medium to a different one. Using the Snell's Law equation, the size of the angle that the light bends can be determined. To determine the angle of refraction, the initial angle of the light and the index of refraction of the two materials must be known.

Scientist with beakers
Scientist with beakers

When waves move from one type of medium to another, from air to water for example, they bend or change direction. This phenomenon is called refraction. The reason the bending occurs is because waves travel at different speeds in different materials. Light is one example of a wave that is refracted when it moves through different media.

The initial and bent angles of a light ray are measured based on the relation to the normal. The normal is a straight line that is perpendicular, or at right angles, to the surface where the light enters the medium. The angle of incidence is the angle that the light makes with the normal on the surface. The angle of refraction is the angle that the light is refracted toward or away from the normal within the new medium.

For instance, a ray of light is traveling through a material with an index of refraction of X and enters another material with an index of refraction of Y. The angle of incidence is x and the angle of refraction would be y. Using the given variables, Snell's Law would be written as: X*sine(x) = Y*sine(y). To find out the angle of refraction, the equation can be rewritten as sine(y) = X*sine(x)/Y or y = arcsin(X*sine(x)/Y).

The density of the medium within which the light is traveling will determine the speed of the light. If the light ray moves into a denser medium, it will slow down, so the ray will bend toward the normal. Bending towards the normal makes the angle of refraction smaller than the angle of incidence. If the light moves into a less dense medium, it speeds up, causing it to bend away from the normal and the angle of refraction will be larger than the angle of incidence.

For example, if a ray of light travels from air to water and enters the water at an angle of 30 degrees, we can use Snell's Law to figure out how much the light will bend, or y. The index of refraction of air is 1, and for water, it is 1.33. Using the equation given earlier, y = arcsin(1*sine(30)/1.33). sine(30) = 0.5, so y = arcsin(0.5/1.33) = 22.1. Thus, the angle of refraction of light entering water at a 30 degree angle is 22.1 degrees.

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thank you a lot.


Snells law also applies to sound and is used to produce angle search units. ksbp

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