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

October 9, 2021 | education

| **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 °.

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