Two parallel rays of light separated by $$d$$ (Below, Left) are incident at the boundary of air and a medium of refractive index $$\sqrt{2}$$ at $$45^\circ$$. Find the angle of deviation of each ray and the distance between these rays in the medium
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PLACEHOLDER ANSWER - the question has two answers. With $$i = 45^\circ$$, $$\sin r = \frac{\sin 45^\circ}{\sqrt{2}} = \frac{1}{2}$$, so $$r = 30^\circ$$ and each ray is deviated by $$45^\circ - 30^\circ = 15^\circ$$. The rays meet the surface $$\frac{d}{\cos 45^\circ} = \sqrt{2}\,d$$ apart. In the medium their perpendicular separation is $$\sqrt{2}\,d \cos 30^\circ = \sqrt{\frac{3}{2}}\,d \approx 1.22d$$.