Given is a thin convex lens of glass (refractive index ) and each… - Vidyadip

MCQ

Given is a thin convex lens of glass (refractive index $\mu$ ) and each side having radius of curvature R . One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself.

A
$R / \mu$
B
$R /(2 \mu-3)$
C
$\mu R$
✓
$R /(2 \mu-1)$

✓

Answer

Correct option: D.

$R /(2 \mu-1)$

(D) $R /(2 \mu-1)$
$
\begin{array}{l}Sol.\
P_{e q}=2 P_{\ell}+P_m \\
-\frac{1}{f_Q}=\frac{2}{f_f}-\frac{1}{f_m} \\
=\frac{4(\mu-1)}{R}-\frac{2}{-R}=\frac{1}{R}(4 \mu-4+2) \\
-\frac{1}{f_{e q}}=\frac{1}{R}(4 \mu-2) \\
\Rightarrow \frac{1}{f_{e q}}=\frac{-1}{R}(4 \mu-2) \\
f_{e q}=\frac{R}{2} \\
R=2 f_{e q}=-2\left(\frac{R}{4 \mu-2}\right)=\frac{-R}{(2 \mu-1)}
\end{array}
$

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