Each dark fring away from the center represents a path difference of one wavelength between the reflection from the gl and from underlying surface. So the 100th ring has a path 100 wavelengths longer. The path difference is two times the height of the gl above the surface. So, 2 * h = 100 (wavelength). Solve for h. Then note that h is the difference between r and r cos. Solve h = r(1-cos θ) for θ. Finally, R= r sin θ.
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