Unpolarized light is incident on a plane glass surface at an angle of $i=57^{\circ }$. If the reflected light is found to be completely polarized, what is the refractive index of the glass? (Given $\tan (57^{\circ })\approx 1.54$)

Solution

1. According to Brewster's Law, when light is incident at the polarizing angle $i_p$, the refractive index $n$ is given by $n=\tan (i_p)$.
2. Given that the reflected light is completely polarized at an angle of $i_p=57^{\circ }$, we substitute this value into the formula: $n=\tan (57^{\circ })$.
3. Using the provided value $\tan (57^{\circ })\approx 1.54$, we find that $n\approx 1.54$.
4. Hence the answer is (C).