Find the refracted angle.

Question

The refractive index of glass in 1.5. A ray of light is transmitted from air to glass at an angle of 42. Find the refracted angle.

Answer 1

The angle that the incident ray makes with the normal line is referred to as the angle of incidence. Similarly, the angle that the refracted ray makes with the normal line is referred to as the angle of refraction.

To solve this problem we use Snell's law:

n₁Sin(θ₁)=n₂Sin(θ₂)

Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.

Because we are moving from a denser material with a higher index, we can have a full reflection. The critical angle is the angle of incidence where the angle of reflection is 90 degrees. As mentioned, the light must travel from an optically more dense medium to an optically less dense medium. The critical angle is

θ_c =Sin^-1(n_2/n₁) = 41.8103.

That means we have a full reflection with an angle of 42 degrees. Another way to see this is using Snell's law. The refractive index of air is approximately 1, we can plug the numbers to find

1.5 Sin(42) = 1 Sin(θ₂)

So θ₂ = Sin^-1(number greater than 1) meaning no meaningful solution.