Question

Figure shows two convex lenses $P$ and $Q$ each made up of three different transparent materials. The number of images formed of an object kept on the principal axis of lenses $P$ and $Q$ respectively.

• A. $3$ and $1$
• B. $3$ and $3$
• C. $3$ and $2$
• D. $1$ and $3$

Answer 1

The correct option is A $3$ and $1$

The focal length of each portion of lens corresponding to a certain material will be given by
$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}+\frac{1}{R_2})$
$\therefore \frac{1}{f}\propto (\mu -1)$
$[\because (\frac{1}{R_1}+\frac{1}{R_2})\text{is constant for all lenses}]$
Thus, for lens $P$, three different portions passes three different focal lengths and hence corresponding to the same object distance there will be three images for each.
For lens $Q$, the combination of the three lenses would effectively act as a single lens and hence only one image is formed.