Question

Two lenses A and B have focal lengths of +20 cm and, −10 cm, respectively.
(a) What is the nature of lens A and lens B?
(b) What is the power of lens A and lens B?
(c) What is the power of combination if lenses A and B are held close together?

Answer 1

(a) The focal length of lens A is +20 cm. The positive sign indicates that lens A is convex, i.e., a converging lens.
The focal length of lens B is -10 cm. The negative sign indicates that lens B is concave, i.e., a diverging lens.

(b) Focal length of lens A, f_A = +20 cm = +0.20 m

∴ Power of lens A, ${\mathit{\text{P}}}_A\text{=}\frac{\text{1}}{{\mathit{\text{f}}}_A}\text{=}\frac{\text{1}}{\text{0.20}}\text{=5 D}$.

Focal length of lens B, f_B = -10 cm = -0.10 m

∴ P​ower of lens B, ${\mathit{\text{P}}}_B\text{=}\frac{\text{1}}{{\mathit{\text{f}}}_B}\text{=}\frac{\text{1}}{\text{-0.10}}\text{=-10 D}$.

(c) When lenses are combined, the power of the combination is the algebraic sum of the powers of the individual lenses.
∴ Power of combination of lens A and B, P = P_A + P_B
P = 5 D - 10 D = - 5 D.