At an angle of incidence of 60 degrees, the angle of refraction is 40 degrees.

At an angle of incidence of 60 degrees, the angle of refraction is 40 degrees. Determine the angle of refraction in this environment if the angle of incidence is 30 degrees.

In accordance with the law of refraction, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value for two media. This value is called the refractive index:

n = sinα / sinβ.

Then, for the two considered cases, we have:

n = sinα1 / sinβ1 = sinα2 / sinβ2,

whence the angle of refraction in the second case is

β2 = arcsin (sinβ1 * sinα2 / sinα1);

β2 = arcsin (sin40 ° * sin30 ° / sin60 °) = arcsin (0.643 * 0.500 / 0.866) = arcsin (0.371) = 21.8 °.