# Angle of Incidence with partial reflection and partial refraction

skibum143

## Homework Statement

A beam of light in air strikes a piece of glass (n=1.51) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the angle of refraction.

## Homework Equations

n1sintheta1 = n2sintheta2

## The Attempt at a Solution

The angle of reflection equals the angle of incidence, which is twice the angle of refraction.
Therefore, I set up the equation as:
1 * sin (2theta) = 1.51 * sin (theta)
But when I try to solve for theta I get that they cancel out (sin 2theta / sin theta) just equals 2? I think I'm doing the trig wrong but I don't know why?

AtticusFinch
Yeah you are doing the trig wrong. You cannot just take the 2 out of the sin function and cancel.

Use this trig identity: sin(2x) = 2 sin x cos x

skibum143
yep, I'm awful at trig so that isn't surprising. haha.

i'm still not getting it right though: if i use that identity, i get:

1 * 2 sin theta cos theta = 1.51 * sin theta

If I divide the left by sin theta, the sin theta cancels out (right???), leaving me:
2 cos theta = 1.51
which gives me a theta of 40.97 deg, which is wrong...

Not sure what I'm doing wrong now...

AtticusFinch
You need to double that angle, they ask for the angle of incidence not the angle of refraction.

skibum143
right. I'm an idiot. thanks for your help!

AtticusFinch
Yep no problem.