In the figure shown, for an angle of incidence \( 45^{\circ} \), at the top surface, what is the...

In the figure shown, for an angle of incidence \( 45^{\circ} \), at the top surface, what is the minimum refractive index needed for total internal reflection at vertical face?
(A) \( \frac{\sqrt{2}+1}{2} \)
(B) \( \sqrt{\frac{3}{2}} \)
(C) \( \sqrt{\frac{1}{2}} \)
(D) \( \sqrt{2}+1 \)