Two plano – convex lenses of glass of refractive index 1.5 cm have radii of curvature of 20 and 30 cm. They are placed in contact with curved surfaces towards each other and the space between them is filled with a liquid of refractive index (4/3). Find the focal length of the system

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$- 72 cm$

36 cm

72 cm

$- 36 cm$

answer is C.

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Detailed Solution

$\begin{array}{l} f_{1} = (\frac{R_{1}}{μ_{g} - 1}) = \frac{20}{1.5 - 1} = 40 cm \\ f_{2} = \frac{30}{1.5 - 1} = 60 cm \\ \frac{1}{f_{3}} = - (μ_{l} - 1) (\frac{1}{R_{1}} + \frac{1}{R_{2}}) \\ = - (\frac{4}{3} - 1) (\frac{1}{20} + \frac{1}{30}) = - \frac{1}{3} (\frac{3 + 2}{60}) \\ f_{3} = - 36 cm \\ \frac{1}{F} = \frac{1}{F_{1}} + \frac{1}{F_{2}} + \frac{1}{F_{3}} = \frac{1}{40} + \frac{1}{60} - \frac{1}{36} \\ F = + 72 cm \end{array}$