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

Answer 1

The correct option is B $sinx=\frac{5}{8}sin\theta$

We have,
$\mu sin\theta =1.01\mu sin{\theta }_1=1.02\mu sin{\theta }_2=....=1.6\mu sinx$
$\Rightarrow \mu sin\theta =1.6\mu sinx$
$\Rightarrow sin\theta =\frac{8}{5}sinx$