Question

A parallel beam of light is incident on a glass prism in the shape of a quarter cylinder of radius $R=0.05m$ and refractive index $n=1.5$ placed on a horizontal table as shown in the figure. Beyond the cylinder, a patch of light is found whose nearest distance $x$ from the cylinder is

• A. $(3\sqrt{3}-4)\times {10}^{-2}m$
• B. $(3\sqrt{2}-2)\times {10}^{-2}m$
• C. $(3\sqrt{5}-5)\times {10}^{-2}m$
• D. $(3\sqrt{2}-3)\times {10}^{-2}m$

Answer 1

The correct option is C $(3\sqrt{5}-5)\times {10}^{-2}m$

$\sin c=\frac{1}{\mu }=\frac{2}{3}$
$\cos c=\frac{R}{R+x}$
$\sqrt{1-\frac{4}{9}}=\frac{R}{R+x}$
$\frac{\sqrt{5}}{3}=\frac{R}{R+x}$
$x=(3\sqrt{5}-5)\times {10}^{-2}m$