by ObviousManiac
Tags: prism, prisms, refraction, snell's law
 P: 37 1. The problem statement, all variables and given/known data 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? 2. Relevant equations n$_{1}$sinø$_{1}$ = n$_{2}$sinø$_{2}$ 3. 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?!?!?
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P: 26,157
Hi ObviousManiac!
 Quote by ObviousManiac 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?!?!?
sin(45° - a) = … ?
P: 37
 Quote by tiny-tim Hi ObviousManiac! Learn your trigonometric identities … sin(45° - a) = … ?
okay so sin(45˚ - a) = sin(45)cos(a) - cos(45)sin(a)

but I'm not sure where to take it from there...
I tried setting up something like:

sin(45)/sin(34) = sin(a)/sin(b)
sin(45)/sin(34) = sin(a)/sin(45-a)
sin(45)/sin(34) = sin(a)/[sin(45)cos(a) - cos(45)sin(a)]

but I don't even know if any of that ^^ is right, I could be going in a totally wrong direction.

HW Helper
Thanks
P: 26,157

Hi ObviousManiac!
 Quote by ObviousManiac first refraction: sin45 = n sin a
 Quote by ObviousManiac okay so sin(45˚ - a) = sin(45)cos(a) - cos(45)sin(a)
Substitute from the first equation into the second.
P: 37
 Quote by tiny-tim Hi ObviousManiac! Substitute from the first equation into the second.
Sin(45-a) = nsin(a)cos(a) - cos(45)sin(a)

...doesn't this just introduce a new variable? (n?)

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