Light traveling in a medium of index of refraction n1 is incident on another medium having an index of refraction n2. Under which of the following conditions can total internal reflection occur at the interface of the two media?(Select all that apply).
a.)The indices of refraction have the relation n2 n1.
b.)The indices of refraction have the relation n1 n2
c.)Light travels slower in the second medium than in the first.
d.)The angle of incidence is less than the critical angle.
e.)The angle of incidence must equal the angle of refraction.

Question

Light traveling in a medium of index of refraction n1 is incident on another medium having an index of refraction n2. Under which of the following conditions can total internal reflection occur at the interface of the two media?(Select all that apply).
a.)The indices of refraction have the relation n2 > n1.
b.)The indices of refraction have the relation n1 > n2
c.)Light travels slower in the second medium than in the first.
d.)The angle of incidence is less than the critical angle.
e.)The angle of incidence must equal the angle of refraction.

anonymous · Answer

$$n1 \sin(\theta_1) = n2\sin(\theta_2) $$
$$\sin(\theta_2) = \frac{n1}{n2} \sin(\theta_1)$$

For total internal reflection, the angle of refraction should go to pi/2 radians at the critical angle, and then have no real solutions for greater angles of incidence. So, at the critical angle, 

$$ sin^{-1}(\frac{n_1}{n_2} \sin(\theta_1)) = \pi/2$$

So what must $$\frac{n1}{n2} \sin(\theta_1) $$
be?
What does that imply about the relative magnitudes of n1 and n2?