Question regarding optics(prism)

[shakeysg]

Homework Statement

figure shows a 90 degrees triangular prism of refractive index n whereby light enters at point A with an incident angle of θ. The light then refracts at point B with an angle of refraction of 90 degrees.

determine index of refraction, n in terms of θ. refer to figure attached.

Homework Equations

using snell's law of refraction,

n.sinθ=n₁.sinθ₁

The Attempt at a Solution

first I used an snell's law to get an eqn

1.sinθ=n.sinθ₁----------------------(1)

using properties of angles and triangles I got
θ₂, θ₃ and θ₄.
θ1=θ3, θ2=θ4.

using snell's law again I got
n.sinθ4=1.sin 90 degrees
n.sinθ4=1

I tried using trigonometry to compute the thetas together and eventually eliminate θ1. But I was not able to do so. Am I missing something?
Since I got stuck, I thought if θ1=45 degrees, getting n in terms of θ is not a problem. But I reasoned to myself that it cannot be possible as I do not know θ4 and n. So making an assumption is not right. I think? I could be wrong though.. hmm..

help would be greatly appreciated and I am sorry if posted anything wrongly such as the format or thought process since this is the first time I am posting.

Thanks!

Syeh

 

[kuruman]

You have two equations

sinθ = n sinθ₁
n sinθ₄ = 1

Can you find a relation between θ₁ and θ₄?

 

[shakeysg]

hmm.. thanks for replying.. I went through that before.. basically 1=ncosθ1 since 90 degrees-θ4=θ1=θ3. and if i were to combine both eqns together, it will result in

sinθ=tanθ1.

the thing is I couldn't eliminate θ1 but I eliminated n instead. I even tried substituting other values of relevant θ into the equation and it got me more irritated. It feels like I am missing something right before my eyes and I cannot comprehend what is it that I missed. oh man. Anyway, this qns is the first part of a 4 parts 12 marks qns. So the solution shouldn't be too complicated. Thanks for replying again.

 

[ehild]

basically 1=ncosθ1

So cosθ1=1/n. What is sinθ1 in terms of n?

ehild

 

[shakeysg]

oh my. hahaa. thanks for making me rethink the qns. i managed to n in terms of theta. thanks again! : D