Explanation

For an equilateral prism, the prism angle is:

$$ A = 60^\circ $$

If the emergent ray grazes the surface, then the angle of emergence is $90^\circ$. Hence, the angle of incidence at the second surface equals the critical angle.

Critical angle $C$ is given by:

$$ \sin C = \frac{1}{\mu} $$

Given refractive index $\mu = \sqrt{2}$:

$$ \sin C = \frac{1}{\sqrt{2}} $$

$$ C = 45^\circ $$

Let $r_1$ be the angle of refraction at the first surface and $r_2$ at the second surface. For a prism:

$$ r_1 + r_2 = A $$

$$ r_1 + 45^\circ = 60^\circ $$

$$ r_1 = 15^\circ $$

Therefore, the angle of refraction at the incident surface is close to 15°.

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