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=$\left(\frac{5}{9}\right)sin\theta$
• D. sin x=$\frac{101}{160}sin\theta$

Answer 1

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

Refractive index and angle of incidence in initial medium is given by $\mu$ and $\theta$ respectively.
Similarly for the final medium, Refractive index and angle of emergence is given by $1.6\mu$ and $x$ respectively.
As, $\frac{\mu }{1.6\mu }=\frac{sin\left(x\right)}{sin\left(\theta \right)}$
So, $sin\left(x\right)=\frac{5}{8}sin\left(\theta \right)$