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# A glass convex lens of refractive index $\large\frac{3}{2}$ has got a focal length equal to $50 \;cm$ Find the focal length of lens if it is immersed in ethyl alcohol of $refractive index \;1.36$

$(a)\;142.75 \;cm \\ (b)\;262.75\;cm \\ (c)\;382.75\;cm \\ (d)\;242.75\;cm$

According to lens makers formula
$\large\frac{1}{f} = \bigg(\large\frac{\mu_2}{\mu_1}-1\bigg) \bigg[ \large\frac{1}{R_1}- \frac{1}{R_2}\bigg]$
$\large\frac{1}{f}$$=(1.5-1) \bigg( \large\frac{1}{R_1}- \frac{1}{R_2}\bigg)$
In ethyl alhocol
$\large\frac{1}{t_{liquid}}= \bigg( \large\frac{1.5}{1.36}-1 \bigg) \bigg[ \frac{1}{R_1}-\frac{1}{R_2}\bigg]$
So $f_{liquid}= \large\frac{(1.5 -1)}{\bigg( \large\frac{1.5-1}{1.36}\bigg)} \times f$
$\qquad= 242.75\;cm$
Hence d is the correct answer.