Snells law

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Snell's law is the simple formula used to calculate the refraction of light when travelling between two media of differing refractive index. Named for its discoverer, Dutch mathematician Willebrord van Roijen Snell (1580-1626).

In the diagram above, two media of refractive indices n1 (on the left) and n2 (on the right) meet at a surface or interface (vertical line). A light ray PO in the leftmost medium strikes the interface at the point O. From point O, we project a straight line at right angles to the line of the interface; this is known as the normal to the surface (horizontal line). The angle between the normal and the light ray PO is known as the angle of incidence, θ1.

The ray continues through the interface into the medium on the right; this is shown as the ray OQ. The angle with which is makes to the normal is known of as the angle of refraction, θ2.

Snell's law gives the relation between the angles θ1 and θ2:

n1 / sin (θ1) = n2 / sin(θ2).

Note that, for the case of θ1 = 0° (i.e., a ray perpendicular to the interface) the solution is θ2 = 0° regardless of the values of n1 and n2. In other words, a ray perpendicular entering a medium perpendicular to the surface is never bent.

A handy rule of thumb is that, for a ray going from a medium with low n (such as air) into a medium with higher n (such as glass), the ray always bends towards the normal of the surface.

When moving from a dense to a less dense medium (i.e. n1>n2), it can be shown that the above equation has no solution when θ1 exceeds a value known as the critical angle:

θcrit = arcsin ( n2 / n1) .

When θ1crit, no refracted ray appears, and the incident ray undergoes total internal reflection from the interface.

See also Fresnel equations.