A ray of light incident at the boundary of two media travels along the path shown (figure B, below). Find the angle (in degrees) in the denser medium if the angle in the rarer medium is doubled.
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From the figure the ray makes $$45^\circ$$ with the normal in medium 1 and $$30^\circ$$ in medium 2, so medium 2 is denser and $$\frac{\mu_2}{\mu_1} = \frac{\sin 45^\circ}{\sin 30^\circ} = \sqrt{2}$$. Doubling the angle in the rarer medium makes it $$90^\circ$$. Then $$\sin r = \frac{\sin 90^\circ}{\sqrt{2}} = \frac{1}{\sqrt{2}}$$, so the angle in the denser medium is $$45^\circ$$.