The critical angle for a glass is 41 degrees. Calculate its refractive index.
Firstly we must remind ourselves of what is meant by critical angle. The critical angle is the angle of incidence beyond which rays of light passing through a denser medium to the surface of a less dense medium are no longer refracted but totally reflected (easily represented on a diagram).
So in our equation for refraction we can substitute in n2 = 1 (because air has a refractive index of 1) and 𝜃1 = 41. We also know that 𝜃2 = 90 degrees because it is the critical angle which is the point at which the angle of refraction is 90 degrees. sin90 = 1 so 𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2 becomes n1 x sin41 = 1. So the refractive index of the glass (n1) = 1/sin41 = 1.524. Because we have only been given information to two significant figures in the question, we leave our answer as 1.5.
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