Question

Two concave lenses L₁ and L₂ are kept in contact with each other. If the space between the two lenses is filled with a material of smaller refractive index, the magnitude of the focal length of the combination
(a) becomes undefined
(b) remains unchanged
(c) increases
(d) decreases.

Answer 1

(c) increases

The focal length of the combination will increase. For finding out the combination of lens we have the formula:
$\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{\mathrm{d}}{f_1{f}_2}$
Where, F is the focal length for the combination
d is the separation between two lenses
Here, d = 0
$$\begin{gathered} \frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2} \\ F=\frac{f_1{f}_2}{f_1+f_2} \end{gathered}$$
Hence, the focal length will increase.