Snells law

Snell's law is the simple formula used to calculate the refraction of light when travelling between two media of differing refractive index.

               P      interface
                *     |
                 *    |
                . *   |
    n1        .    *  |               n2
             .  A1  * |
             .       *|
  - - - - - - - - - - O - - - - - - - - - - - normal
                      |*   A2 .
                      |  *    . 
                      |    * .
                      |      *
                      |        *
                      |          Q
                           

In the diagram above, two media of refractive indexes 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, A₁.

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, A₂.

Snell's law gives the relation between the angles A₁ and A₂:

n₁ / sin (A₁) = n₂ / sin(A₂).

Note that, for the case of A₁ = 0° (i.e., a ray perpendicular to the interface) the solution is A₂ = 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.

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