Two plano concave lenses of glass of refractive index 1.5 have radii of curvature 20 cm and 20 cm 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 $\frac{5}{3}$ . The focal elngth of the combination is (in cm)

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answer is D.

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Detailed Solution

$\frac{1}{f_{1}} = (μ_{g} - 1) (\frac{- 1}{R})$

$\frac{1}{f_{2}} = (μ_{l} - 1) (\frac{2}{R})$

$\frac{1}{f_{3}} = (μ_{g} - 1) (\frac{- 1}{R})$

$\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}} + \frac{1}{f_{3}}$ = $= (1.5 - 1) (\frac{- 1}{20}) + (\frac{5}{3} - 1) (\frac{2}{20}) + (1.5 - 1) (\frac{- 1}{20})$

f=60cm

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