# Determining refractive index

1. Nov 11, 2009

### Neophyte7

A ray of light strikes a square glass block at an angle of 45 degrees and enters the glass. If this block is surrounded by air (n=1), what is the minimum value of the refractive index of the glass if the total internal reflection occurs at point P. (see attached diagram)

I'm really lost on this one. I know to take Snell's law at the surface AD. And the condition for the total internal reflection at the surface AB.

I know n1sin(45) = n2sin(theta) from Snell's law, but how do I get the value for the unknow angle (theta)?

I know that we can determine that the angle at P is sin(90-theta) which = cos (theta)
And I know that sin2(theta) + cos2(theta) = 1. But that's as far as I can get.

Any help would be appreciated. I've attached a diagram for clarification. Thanks.

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• ###### diagram1.jpg
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2. Nov 11, 2009

### mgb_phys

Normally you don't - it's difficult to measure the path of the light inside the glass.
Draw the path of the light ray coming out of the bottom side of the block - then try finding 'n' in terms of the displacement of the ray and the thickness of the block.

3. Nov 11, 2009