Math Root

Refraction

Wilibrord Von Snell found the law for refraction when light goes from medium 1 with index of refraction n1 to medium 2 with index of refraction n2. The angles q are measured from the perpendicular to the surface.

n1 sin q 1 = n2 sin q 2

Simple geometry can be used to show that if you place a layer of index of refraction n3 between the two original layers your answer will not change.

Do the math!

The relation between q 1 and q 2 is found from Snell's law. The angles are measured from the perpendicular to the surface.

Geometry gives the relation between q3 and q3'.

Notice that the surfaces between n1 and n3 and between n3 and n2 are parallel.

This means hat the perpendiculars to these lines are also parallel.

The light beam in medium 3 crosses these parallel lines.

From geometry, q3 = q3'

Then use snell's law again between layers 3 and 2.

The final result is

n1 sin q 1 = = n3 sin q 3 = n2 sin q 2

or

n1 sin q 1 = n2 sin q 2

the same result as when light goes directly from medium 1 to medium 3.