# Angle of Incidence with partial reflection and partial refraction

#### skibum143

1. 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.

2. Homework Equations
n1sintheta1 = n2sintheta2

3. 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?

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#### 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!

Yep no problem.