Question

A convex lens has a focal length of $0.5m$. It has to be combined with a second lens, so that the combination has a power of $1.5$ dioptre. Which of the following could be the second lens?

• A. A concave lens of focal length $2m$
• B. Another convex lens of focal length $0.5m$
• C. A concave lens of focal length $0.5m$
• D. A convex lens of focal length $2m$

Answer 1

Answer: (A)

A concave lens of focal length $2m$

Power of combination $P=1.5$ dioptre

Power of convex lens having focal length of $0.5m$, $P_1=\frac{1}{0.5}$ dioptre

Using $P=P_1+P_2$

$\therefore$ $1.5=\frac{1}{0.5}+P_2$

We get $P_2=-0.5$ dioptre

Thus focal length of second lens $f_2=\frac{1}{P_2}$

$⟹$ $f_2=-\frac{1}{0.5}=-2m$ (negative sign implies the lens must be a concave lens)

Thus second lens could be concave lens of focal length $2m$.