Question

A quarter cylinder of radius $R$ and refractive index $1.5$ is placed on a table. A point object P is kept at a distance of $mR$ from it. The value of ${}^{\prime }{m}^{\prime }$ for which a ray from P will emerge parallel to the table, as shown in figure, is

• A. $4/3$
• B. $3/4$
• C. $3/2$
• D. $2/3$

Answer 1

The correct option is A $4/3$

Applying the lens formula for the plane surface,

$\frac{1.5}{v_1}-\frac{1}{-mR}=\frac{1.5-1}{\infty }$

Solving, gives $v_1=-\left(1.5mR\right)$

Now, again applying the lens formula for the curved surface,

$\frac{1}{\infty }-\frac{1.5}{-(1.5mR+R)}=\frac{1-1.5}{-R}$

Solving for $m$, gives us the value of $m$ as $\frac{4}{3}$