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(D) The focal length $f$ of a lens is given by the Lens Maker's formula:$\frac{1}{f} = \left( \frac{n_L}{n_m} - 1 \right) \left( \frac{1}{R_1} - \frac

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$L_2$ and immersed in $L_1$

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(D) The focal length $f$ of a lens is given by the Lens Maker's formula:$\frac{1}{f} = \left( \frac{n_L}{n_m} - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$where $n_L$ is the refractive index of the lens material and $n_m$ is the refractive index of the surrounding medium.For a double concave lens,the term $\left( \frac{1}{R_1} - \frac{1}{R_2} \right)$ is negative.For the lens to diverge light,it must act as a concave lens,meaning its focal length $f$ must be negative.Since $\left( \frac{1}{R_1} - \frac{1}{R_2} \right) This implies $\frac{n_L}{n_m} > 1$,or $n_L > n_m$.In option $(d)$,the lens is filled with liquid $L_2$ (refractive index $n_2$) and immersed in liquid $L_1$ (refractive index $n_1$). Since $n_2 > n_1$,the condition $n_L > n_m$ is satisfied,and the lens will diverge the light.

$A$ hollow double concave lens is made of very thin transparent material. It can be filled with air or either of two liquids $L_1$ and $L_2$ having refractive indices $n_1$ and $n_2$ respectively $(n_2 > n_1 > 1)$. The lens will diverge a parallel beam of light if it is filled with

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