A convex lens of focal length 20 cm and two concave lenses of focal length 10 cm and 30 cm are placed in contact with each other. The focal length of the combined three lenses will be.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → -12 cm
For thin lenses in contact the powers add, so \( \frac{1}{F} = \frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3} \). A convex lens has a positive focal length and a concave lens a negative one.
\( f_1 = +20\,\mathrm{cm},\quad f_2 = -10\,\mathrm{cm},\quad f_3 = -30\,\mathrm{cm} \)
\( \displaystyle \frac{1}{F} = \frac{1}{20}-\frac{1}{10}-\frac{1}{30} = \frac{3-6-2}{60} = -\frac{5}{60} = -\frac{1}{12} \)
\( F = -12\,\mathrm{cm} \)
The negative sign shows that the combination behaves as a diverging lens.