Problem 5.165

Two parallel plane-polarized beams of light of equal intensity whose oscillation planes $N_{1}$ and $N_{2}$ form a small angle $\varphi$ between them (Fig. 5.30) fall on a Nicol prism. To equalize the intensities of the beams emerging behind the prism, its principal direction $N$ must be aligned along the bisecting line $A$ or $B$. Find the value of the angle $\varphi$ at which the rotation of the Nicol prism through a small angle $\delta \varphi \ll \varphi$ from the position $A$ results in the fractional change of intensities of the beams $\Delta I / I$ by the value $\eta=100$ times exceeding that resulting due to rotation through the same angle from the position $B$.