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

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

Another convex lens of focal length 60 cm is placed at a distance of 30 cm from the first lens

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

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

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 30 cm
or $\frac{1}{30} = \frac{1}{20} + \frac{1}{f}$

i,e., when another concave lens of focal length 60 cm 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
$\frac{1}{20} = (\frac{3}{2} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}}) .......... (1) \frac{1}{30} = (\frac{3 / 2}{μ} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}}) .............. (2)$

From Equation (1) and (2), we get

$μ = \frac{9}{8}$