Physics---Total Internal Reflection?

Question

Which of the following must be true if total internal reflecation is to occur?
I. The angle of incidence must be smaller than a certain maximum angle determined by the refractive indices of the two media
II. Light rays must travel from denser material to lighter one
III. The sine of the refracted angle must be less than one

Answer 1

II.

I. and III. are both the opposites of the required conditions. This is clearest from III - if the sine of the refracted angle is less than 1, refraction will occur at the indicated angle. If it is greater than 1, no such angle exists and refraction is not possible, so we get total internal reflection.

It follows that for total internal reflection we need the sine of the angle of incidence to be greater than a certain amount, and hence the angle of incidence to be greater than a certain angle, the opposite of statement I.

By contrast, II must hold: we need
sin r = sin i . n1 / n2 > 1
but since sin i < 1 by definition, we must have n1 / n2 > 1 and hence n1 > n2. Generally speaking this correlates with density, so the first material must be denser than the second.

Answer 2

The angle of incidence is always equal to the angle of reflection, whether you have total internal reflection or not. For total internal reflection at 45 degrees, the ratio of the indexes of refraction of the two media must be sin(45), or 1/sqrt(2), with the light originating in the medium with the higher index of refraction.