Three convex lenses of focal lengths 10 cm, 30 cm and 60 cm and two concave lenses of focal lengths 20 cm and 40 cm are placed in contact co-axially. The power of the combination of the lenses is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 7.5 D
Thin lenses placed in contact behave as one lens whose power is the sum of the individual powers. With the focal length in centimetres, the power in dioptres is 100/f; a convex lens has a positive focal length and a concave lens a negative focal length.
\( \displaystyle P = \frac{100}{f_1} + \frac{100}{f_2} + \frac{100}{f_3} + \frac{100}{f_4} + \frac{100}{f_5} \)
\( \displaystyle P = \frac{100}{10} + \frac{100}{30} + \frac{100}{60} + \frac{100}{-20} + \frac{100}{-40} \)
\( P = (10 + 3.33 + 1.67 - 5 - 2.5)\,\mathrm{D} \)
\( P = 7.5\,\mathrm{D} \)