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## Homework Statement

A horizontal beam of light enters a 45-90-45 prism at the center of it's long side, as shown below. The emerging ray moves in a direction that is 34˚ below the horizontal. What is the index of refraction for the prism?

## Homework Equations

n[itex]_{1}[/itex]sinø[itex]_{1}[/itex] = n[itex]_{2}[/itex]sinø[itex]_{2}[/itex]

## The Attempt at a Solution

n1 x sin(i) = n2 x sin(r1): (1st refrection)

and n2 x sin(r2) = n1 x sin(34˚): (2nd refraction)

^^Here n1 is the refractive index of air, n2 is the refractive index of prism, r1 and r2 are the angles of reflection at the two surfaces, and i is the incidence angle.

r1 + r2 = 45˚ or r2 = 45˚ - r1.

Substituting the above value of r2 in the equation(2),we get

n2 x sin(45 - r1) = 1 x sin(34˚)

...and then I'm stuck!

To simplify what I've figured out:

first refraction: sin45 = n sin a

second refraction: n sinb = sin34

and using geometry: a + b = 45

BUT HOW DO I FIND a and b?!?!?