Calculating Reflected Light Displacement in Glass

[MarieWynn]

Homework Statement

A beam of light makes an angle of 26 o with the normal of a mirror made of 2.4- mm-thick glass silvered on the back. If the index of refraction of the glass is 1.50, how far is the point at which the beam leaves the glass surface (after being reflected from the silver backing) from the point at which the beam entered the glass? ( mm)

Homework Equations

I thought this was a displacement problem, so these are the equations I used:
Snell's Law: n₁sintheta₁=n₂sintheta₂
Displacement: sin(theta₂-theta₁=d/h

The Attempt at a Solution

I used h=2.4/sintheta₁ to find the hypotenuse after using Snell's law to find theta₁ (16.99deg). Then I plugged the numbers into the displacement formula to find d, which I found to be 0.393mm. My homework says this is incorrect, though.

I am completely lost as to how I am going wrong here. Would this not be displacement? This is preparation for my final exam, so if someone could point me in the right direction rather than go over any formulas, that would be appreciated. I want to find the answer myself so I can be sure I know it for the final. Thanks!

 

[Liquidxlax]

it is really good to draw and exaggerated diagram of the light path through the glass reflecting off the silver then leaving the glass. Using angle relations and snell's law.

knowing the angles from snell's law and using your basic trig. it's an easy enough problem