How Does Glass Thickness Affect Refractive Index Calculation?

[kent davidge]

Homework Statement

Old photographic plates were made of glass with a lightsensitive emulsion on the front surface. This emulsion was somewhat transparent. When a bright point source is focused on the front of the plate, the developed photograph will show a halo around the image of the spot. If the glass plate is 3.10 mm thick and the halos have an inner radius of 5.34 mm, what is the index of refraction of the glass? (Hint: Light from the spot on the front surface is scattered in all directions by the emulsion. Some of it is then totally reflected at the back surface of the plate and returns to the front surface.)

Homework Equations

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The Attempt at a Solution

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Is my sketch for the situation correct? I found n = 1.532 and the book answer is also 1.53.
Since the reflected ray is tangent to the upper end of halo, I assumed the ray reflecting half-way in the back surface. Is it correct?

 

[Rx7man]

I think that's right.. the angle of incidence is always equal to the angle of reflection.