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?

#### Solution

(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, P_A=1/(f_A)=1/0.20=5D`

Focal length of lens B,* **f*_{B} = -10 cm = -0.10 m

∴ Power of lens B, `P_B=1/f_b=1/-0.10=-10D`

(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=5D-10D=-5D.`