Q: 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} or L_{2} having refracting 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

(A) air and placed in air

(B) air and immersed in L1

(C) L1 and immersed in L2

(D) L2 and immersed in L1

Ans: (D)

Sol: According to lens maker’s formula

$\large \frac{1}{f} = (\frac{n_L}{n_m} – 1)(\frac{1}{R_1} – \frac{1}{R_2})$

In case of double concave

$ (\frac{1}{R_1} – \frac{1}{R_2})$ will be negative .

For lens to be diverging in nature $(\frac{n_L}{n_m} – 1)$ should be +ve or n_{L} > n_{m}

But here , n_{2} > n_{1} , therefore Lens should be filled with L_{2} and immersed in L_{1}