A thin equiconvex lens is made of glass of refractive index 1.5 and its focal length in air is 0.2 m. If it acts as a concave lens of 0.5 m focal length when dipped in a liquid, the velocity of light in the liquid is

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$2.4 \times 10^{8} {ms}^{- 1}$

$1.2 \times 10^{8} {ms}^{- 1}$

$1.6 \times 10^{8} {ms}^{- 1}$

$1.8 \times 10^{8} {ms}^{- 1}$

answer is B.

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Detailed Solution

$\frac{f_{l}}{f_{a}} = \frac{(μ - 1) μ_{l}}{(μ - μ_{l})}$

$\Rightarrow \frac{- 0 .5}{0 .2} = \frac{(1 .5 - 1)}{1 .5 - μ_{l}} \times μ_{l}$

$\Rightarrow \frac{- 5}{2} = \frac{μ_{l}}{2 (1 .5 - μ_{l})}$

$\Rightarrow - 15 + 10 μ_{l} = 2 μ_{l}$

$\Rightarrow μ_{l} = \frac{15}{8} = \frac{C}{V}$

$\Rightarrow \frac{15}{8} = \frac{3 \times 10^{8}}{V}$

$\Rightarrow V = 1 .6 \times 10^{8} {ms}^{- 1}$

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