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(D) The focal length $f$ of a lens is given by the lens maker's formula: $\frac{1}{f} = (\frac{\mu_l}{\mu_m} - 1)(\frac{1}{R_1} - \frac{1}{R_2})$.For

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filled with $CS_2$ and immersed in water

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(D) The focal length $f$ of a lens is given by the lens maker's formula: $\frac{1}{f} = (\frac{\mu_l}{\mu_m} - 1)(\frac{1}{R_1} - \frac{1}{R_2})$.For a double concave lens,the radii of curvature are $R_1 = -R$ and $R_2 = +R$,so $(\frac{1}{R_1} - \frac{1}{R_2}) = -\frac{2}{R}$.Thus,$\frac{1}{f} = -\frac{2}{R}(\frac{\mu_l}{\mu_m} - 1)$.For the lens to act as a diverging lens,the focal length $f$ must be negative,which implies $(\frac{\mu_l}{\mu_m} - 1) > 0$,or $\mu_l > \mu_m$.In option $(d)$,the lens is filled with $CS_2$ $(\mu_l = 1.6)$ and immersed in water $(\mu_m = 1.33)$.Since $1.6 > 1.33$,the condition $\mu_l > \mu_m$ is satisfied,and the lens acts as a diverging lens.

$A$ hollow lens is made of thin glass and in the shape of a double concave lens. It can be filled with air,water of refractive index $1.33$,or $CS_2$ of refractive index $1.6$. It will act as a diverging lens,if it is

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