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Another little physics porblem

F

Finns14

Golden Member
A prism is made from a certain type of glass has a cross section shaped like an equilateral triangle. The indices of refraction for the red and violet light in this type of glass are 1.602 and 1.626, respectively. The angle of incidence for both the red and violet light is 60.0°. Find the angles of refraction at which the (a) red and (b) violet rays emerge into the air from the prism

Thanks in advanced!
 
You can set up the geometry. Draw it out. Make sure that the triangle is HUGE so that you don't accidentally lose the finer details.

Set it so the triangle is pointing up. Use Snell's law to determine the transmitted angle into the glass. Use some geometry to find the incident angle on the other surface, and then use snell's law again to determine the final transmitted angle at air. Once you've derived the working equation, you can plug and chug. Just assume that the triangle is surrounded by air (it's not resting on a table or something, it's floating using magic).

Remember, an equilateral triangle is composed of 60 degree angles. Once you have the first transmitted angle, you can find the incident angle on the beam as it's about to leave the prism.
 
Here, I'll just do out the math for you because it's easy. I hope you've drawn a picture, that's pretty essential for most optics problems

sin(60) = n*sin(theta1)
theta_2 = 180 - 60 - (90-theta1) = 30+theta1
n*sin(90-theta_2) = sin(theta_answer)

theta_answer is the angle you were asked to find

I'm sure there's some nifty geometric property that would make this even faster, but that's the easiest to understand explanation. You find theta 1, the transmission angle into the glass. Draw the beam as it passes through the glass and you have a new triangle with angles (90-theta1), theta 2, and 60 (a corner of the equilateral triangle). The incident angle is (90-theta2). Use that to find the final transmission angle.
 
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