Question

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 $R.I$. $1.01\mu, 1.02\mu, 1.03\mu, .... ,1.50\mu$ . The ray emerges from the composite plate into a medium of refractive index $1.6\mu$ at 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. $sin\, x= \left(\frac{1.5}{1.01}\right)^{50} sin \,\theta$

Answer 1

Answer: (B)

According to Snell’s law,
$\mu sin \,\theta = 1.6\,\mu sin\,x$
$\therefore sin\,x = \frac{5}{8} sin \theta$