Law of Refraction: Angle of Reflection & Refraction

[jenc305]

This seems really easy but I am having a really hard time getting the correct answer to this question. Any help would be much appreciated.

A ray in air is incident on a glass plate whose index of refraction is 1.60. The angle of refraction is one half the angle of reflection. The angle of refraction is closest to:

I know to use snell's law and theta_a = theta_r but the problem doesn't give me any angles to compute theta_b

(1) sin (theta_a) = 1.60 sin (theta_b)
and
theta_b = 1/2 theta_r = 1/2 theta_a
I'm I suppose to assume something here?

 

[Hootenanny]

Well if you know $\sin\theta_b = \frac{1}{2}\sin\theta_a$, then all you need to do is a subsitution.

 

[topsquark]

Well if you know $\sin\theta_b = \frac{1}{2}\sin\theta_a$, then all you need to do is a subsitution.

Since $$\theta_b=(1/2) \theta_a$$ then
$$sin\theta_a=sin(2\theta_b)=2sin\theta_b*cos\theta_b=1.6sin\theta_b$$
Cancelling the sine terms:
$$2cos\theta_b=1.6$$
etc.

-Dan