For incident light ray to retrace it's initial path, it should fall normally on the silvered surface.
Given, prism angle, A=30∘
Let the angle of incidence be i
From the figure,
x=90−A=60∘
x+r=90∘⇒∠r=30∘
Thus, angle of refraction ∠r=30∘
Now, applying Snell's law at the surface DE, we have
μ=Sin iSin r
Sin i=Sin r×μ
Sin i=Sin 30×√2
i=Sin−1(√22)
i=Sin−1(1√2)
i=45∘
Hence, the answer is OPTION C.