Question

Cross-section of a thick cylinderical pipe of inner radius r and outer radius R is shown in figure. Refractive index of glass of cylinder is $\mu$. A ray AB gracing inner surface after refraction becomes parallel to x -axis, then BC is? All rays are in plane of page.

• A. $(\mu -1)r$
• B. $(\mu -1{)}^{2}R$
• C. $\frac{\mu R^2}{r}$
• D. $\mu r$

Answer 1

The correct option is D $\mu r$


$\frac{1}{\mu }=\frac{\sin i}{\sin r}\Rightarrow \sin r=\mu \sin i\sin i=\frac{r}{R}$
From the diagram, $\theta =90-r$
$\cos \theta =\sin r\Rightarrow \frac{BC}{R}=\sin r\Rightarrow BC=R\sin rBC=R\mu \sin i=\text{/}R\mu \frac{r}{\mathrm{R/}}⟹BC=\mu r$