Question

A rod of glass ($\mu =1.5$) and of square cross section of bent into the shape shown in the figure. A parallel beam of light falls on the plane flat surface $A$ as shown in the figure. If $d$ is the width of side and $R$ is the radius of circular arc then for what maximum value of $\frac{d}{R}$ light entering the glass through surface $A$ emerges from the glass through $B$

• A. $1.5$
• B. $0.5$
• C. $1.3$
• D. None of these

Answer 1

Answer: (B)

$0.5$

Consider the figure if smallest angle of incidence $\theta$ is greater than critical angle then all light will emerge out of $B$
$\Rightarrow \theta \ge {\sin }^{-1}\left(\frac{1}{\mu }\right)\Rightarrow \sin \theta \ge \frac{1}{\mu }$
from figure $\sin \theta =\frac{R}{R+d}$
$\Rightarrow \frac{R}{R+d}\ge \frac{1}{\mu }\Rightarrow (1+\frac{d}{R})\le \mu$
$\Rightarrow \frac{d}{R}\le \mu -1\Rightarrow {\left(\frac{d}{R}\right)}_{max}=0.5$