$A$ ray of light travelling in a medium of refractive index $\mu$ is incident at an angle $\theta$ on a composite transparent plate consisting of $50$ plates of refractive indices $1.01\mu, 1.02\mu, 1.03\mu, \dots, 1.50\mu$. The ray emerges from the composite plate into a medium of refractive index $1.6\mu$ at an angle $x$. Then:

• A
  $\sin x = {\left( {\frac{{1.01}}{{1.5}}} \right)^{50}}\sin \theta $
• B
  $\sin x = \frac{5}{8}\sin \theta $
• C
  $\sin x = \frac{8}{5}\sin \theta $
• D
  $\sin x = {\left( {\frac{{1.5}}{{1.01}}} \right)^{50}}\sin \theta $