A convex lens of focal length 30 cm is in contact with a concave lens of focal length 20 cm. Is the system working as a converging or diverging lens? What is the focal length of the combination?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Diverging, 60 cm
For thin lenses in contact, the powers add, so the reciprocals of the focal lengths add. With the Cartesian sign convention, a convex lens has a positive focal length and a concave lens a negative one.
\( f_1 = +30\,\mathrm{cm} \)
\( f_2 = -20\,\mathrm{cm} \)
\( \displaystyle \frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2} = \frac{1}{30} - \frac{1}{20} = \frac{2 - 3}{60} = -\frac{1}{60} \)
\( \displaystyle F = -60\,\mathrm{cm} \)
The negative focal length means the combination behaves as a diverging lens of focal length 60 cm. The concave lens has the shorter focal length, so it is the stronger lens and decides the nature of the combination.