Optics question - Don't know if anyone can help

[randybryan]

I've attached a screenshot of the question, and I have to admit I'm really struggling. I don't know if anyone will be able to help as optics is very diagram-dependent, but perhaps you can give me a hint without needing to draw anything.

I'm stuck on (ii) a)

The first thing I did was use Snell's law to give sin(α)=n sin(β), and that's about as far as I've got in progress. I realize I need to get sin(β) in terms of θ, but nothing I seem to do can get me the answer. Do I need to consider the angle γ as well? I know that n sinγ≈ 1, but I'm just adding another variable to the problem!

(I have an exam soon, hence the sudden influx of questions)

 

[TSny]

Hello.

See if you can use just geometry to relate the angles β, γ, and θ.

Hint: It might be helpful to draw an auxiliary vertical line through the point where the ray strikes the wall of the cone.

 

[randybryan]

Of course! I put the line in every other place but there. Thanks for the help