Refraction in Isosceles triangle [Uni Phys 2]

[jonathanlv7]

Homework Statement

Suppose the isosceles prism of the figure(http://imgur.com/EQiQSoO) has apex angle φ = 53.4° and index of refraction n = 1.41. (a) What is the smallest angle of incidence θ for which a ray can enter the left face of the prism and exit the right face? (b) What angle of incidence θ is required for the ray to exit the prism with an identical angle θ for its refraction, as it does in the figure?

Homework Equations

snells law -- critical angle

The Attempt at a Solution

For part A - First I made a triangle then I tried to do a bunch of geometry/trig to find the answer and ended up with nothing. Then I tried to use the critical angle formula where the sine(incident) = 1/n and that did not work either. Been working on this for over an hour now so some help would be amazing! Haven't even tried part B yet.

 

[honlin]

For part A, the critical angle that you found is the angle of incident for the second refraction. Why don't you try to find the first angle of refraction using the critical angle you have found?

 

[jonathanlv7]

Yeah I'm looking at it and I can't see how to relate the critical angle to the angle I want. Something I tried which I think is wrong is AngleOfIncident = arcsine(nsin(90-arcsine(1/n)))

 

[honlin]

Try to make a smaller triangle. Make use of the angle of the apex given.

 

[honlin]

Something I tried which I think is wrong is AngleOfIncident = arcsine(nsin(90-arcsine(1/n)))

How do u get this equation?

 

[jonathanlv7]

I got the equation from http://imgur.com/KdlNuLH --- Also, I figured out part B so that's done. TY for helping!

EDIT: I don't think that angle i called 90 degrees is actually 90 degrees

 

[jonathanlv7]

So I worked on it some more and I got this answer - AngleOfIncident is 90 degrees. Is this right? For part A

 

[honlin]

I don't think so, i got a pretty small angle instead of 90, can u show me your working?

 

[jonathanlv7]

Finally! I got! Its arcsine(sin(phi-arcsine(1/n))) = 11.64 --- Thanks for helping me out! I have some other problems I'm going to start on so if you don't mind sticking around the forums for a little that'd be awesome!

 

[honlin]

Haha, you are welcome =) I will try to help with whatever i can but i don't know if i could. I am a student like you too ><