Refraction?

Three sheets of plastic have unknown indices of refraction. Sheet 1 is placed on top of sheet 2, and a laser beam is directed onto the sheets from above so that it strikes the interface at an angle of 26.8° with the normal. The refracted beam in sheet 2 makes an angle of 30.6° with the normal. The experiment is repeated with sheet 3 on top of sheet 2, and with the same angle of incidence, the refracted beam makes an angle of 37.3° with the normal. If the experiment is repeated again with sheet 1 on top of sheet 3, what is the expected angle of refraction in sheet 3? Assume the same angle of incidence.





I've tried 57.1 degrees on my webassign and it is wrong. Any help is appreciated b/c I don't know what to do on this problem anymore. Thanks.

Refraction?
Here's the way I would do the problem:





From experiment 1 (sheet 1/sheet 2) we know that:


n1 * sin(26.8) = n2 * sin (30.6)





From experiment 2 (sheet 3/sheet 2) we know that


n3 * sin(26.8) = n2 * sin(37.3)





The equation for the experiment in question is


n1 * sin(26.8) = n3 * sin θ


and we want to solve for θ.





From the first two equations we have that


n1/n3 = sin(30.6)/sin(37.3)





Plugging this into the equation we are trying to solve we get


sin(30.6)/sin(37.3)*sin(26.8) = sin θ


θ = arcsin (sin(30.6)/sin(37.3)*sin(26.8))


θ = 22.256 degrees
Reply:Wow this is a great question. I'm no help. I thought that the angle of incidence equaled the angle of reflection, so all angles are equal unless they are not exactly parallel. I'm confused.