Suppose you have an unknown clear substance immersed in water, and you wish to identify it by finding its index of refraction. You arrange to have a beam of light enter it at an angle of 45.0º, and you observe the angle of refraction to be 40.3º. What is the index of refraction of the substance and its likely identity?

When light passes from one medium to another at an angle, it may refract, or bend, according to Snell's law:

n₁sin (θ₁) = n₂sin (θ₂)

n₁ = index of first medium, θ₁ = angle of incidence, n₂ = index of second medium, θ₂ = angle of refraction

Given values:

n₁ = 1.33 (water), θ₁ = 45.0°, θ₂ = 40.3°

Plug in and solve for n₂:

1.33sin (45.0°) = n₂sin (40.3°)

n₂ = 1.454

I looked up this value on the HyperPhysics indices of refraction table ... The index we calculated is closest to 1.46, which is that of fused quartz.