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Two Plano concave lenses of glass of refractive index 1.5 have radii of curvature $20 c m$ and $30 c m$ respectively. They are placed in contact with the curved surface towards each other and the space between them is filled with a liquid of refractive index 5/2. The focal length of the combination is (in cm)

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Detailed Solution

From lens maker’s formula, effective focal length is

$\frac{1}{F} = (μ_{1} - μ_{g}) (\frac{1}{R_{1}} + \frac{1}{R_{2}})$

$= (\frac{5}{2} - \frac{3}{2}) (\frac{1}{20} + \frac{1}{30})$

$\frac{1}{F} \Rightarrow \frac{1}{12} \Rightarrow F = 12 c m$

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