A thin convex lens \( L \) (refractive index \( =1.5) \) is placed on a plane mirror \( M \). Wh...

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A thin convex lens \( L \) (refractive index \( =1.5) \) is placed on a plane mirror \( M \). When a pin is placed at \( A \), such that \( O A=18 \mathrm{~cm} \), its real inverted image is formed at \( A \) itself, as shown in figure. When a liquid of refractive index \( \mu_{l} \) is put between
\( \mathrm{P} \)
WV the lens and the mirror, the pin has to be moved to \( A^{\prime} \), such that \( O A^{\prime}=27 \mathrm{~cm} \), to get its inverted real image at \( A^{\prime} \) itself. The value of \( \mu_{l} \) will be
(a) \( \sqrt{3} \)
(2019 Main, 9 April II)
(c) \( \frac{4}{3} \)
(b) \( \sqrt{2} \)
(d) \( \frac{3}{2} \)
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