A point object is at 30 cm from a convex glass lens $(μ_{s} = \frac{3}{2})$ of focal length 20 cm. The final image of object will be formed at infinity, if

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The whole system is immersed in a liquid of refractive index 9/8

The whole system is immersed in a liquid of refractive index 4/3

another concave lens of focal length 60 cm is placed in contact with the previous lens

another concave lens of focal length 60 cm is placed at a distance of 30 cm from the first lens

answer is A, D.

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Detailed Solution

final image is formed at infinity if the combined focal length of the two lenses (in contact) becomes 30cm . Thus from lens maker’s formula, $\frac{1}{30} = \frac{1}{20} + \frac{1}{f}$ i. e when another concave lens of focal length 60 mc is kept in contact with the first lens. Similarly, let $μ$ be the refractive index of a liquid in which focal length of the given lens becomes 30 cm. Then,
$\frac{1}{20} = (\frac{3}{2} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}}) \frac{1}{30} = (\frac{3 / 2}{μ} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

From Eqs (i) and (ii), $μ = \frac{9}{8}$