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>> $A quarter cylinder of radius R and refra$

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 $m R$ from it. The value of $^{'} m^{'}$ for which a ray from P will emerge parallel to the table, as shown in figure, is

6710

A

$4 / 3$

B

$3 / 4$

C

$3 / 2$

D

$2 / 3$

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Updated on : 2022-09-05

Solution

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Correct option is A)

Applying the lens formula for the plane surface,

$\frac{1 . 5}{v _{1}} - \frac{1}{- m R} = \frac{1 . 5 - 1}{\infty}$

Solving, gives $v_{1} = - (1.5 m R)$

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

$\frac{1}{\infty} - \frac{1 . 5}{- ( 1 . 5 m R + R )} = \frac{1 - 1 . 5}{- R}$

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

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