Electrical Physics Question?

Question

A light ray is traveling in a diamond (n = 2.419). If the ray approaches the diamond-air interface, what is the minimum angle of incidence that will result in all of the light being reflected back into the diamond? The index of refraction for air is 1.000.

Answer 1

"When the angle of incidence in water reaches a certain critical value, the refracted ray lies along the boundary, having an angle of refraction of 90-degrees. This angle of incidence is known as the critical angle; it is the largest angle of incidence for which refraction can still occur. For any angle of incidence greater than the critical angle, light will undergo total internal reflection."

So what you want is the critical angle, so you would use the equation - ni*sin(Oi) = nr*sin(Or) where i = incident and r = refracted. Our refracted angle, Or = 90 degrees because we want the angle of incidence that creates a refracted angle of 90 degrees.

This simplifies to ni*sin(Oi) = nr*sin(90)

ni*sin(Oi) = nr

sin(Oi) = nr/ni

Oi = sin^(-1)(nr/ni)

Where nr = index of refraction for the air and ni = index of refraction for diamond.

This gives Oi = 24.42 degrees.