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1. 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.
2. Homework Equations
using snell's law of refraction,
n.sinθ=n_{1}.sinθ_{1}
3. The Attempt at a Solution
first I used an snell's law to get an eqn
1.sinθ=n.sinθ_{1}(1)
using properties of angles and triangles I got
θ_{2}, θ_{3} and θ_{4}.
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
1. Homework Statement
2. Homework Equations
3. The Attempt at a Solution
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.
2. Homework Equations
using snell's law of refraction,
n.sinθ=n_{1}.sinθ_{1}
3. The Attempt at a Solution
first I used an snell's law to get an eqn
1.sinθ=n.sinθ_{1}(1)
using properties of angles and triangles I got
θ_{2}, θ_{3} and θ_{4}.
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
1. Homework Statement
2. Homework Equations
3. The Attempt at a Solution
Attachments

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