Question

(a) What do you understand by the power of a lens? Name one factor on which the power of a lens depends.
(b) What is the unit of power of a lens? Define the unit of power of a lens.
(c) A combination of lenses for a camera contains two converging lenses of focal lengths 20 cm and 40 cm and a diverging lens of focal length 50 cm. Find the power and focal length of the combination.

Answer 1

the reciprocal if focal length.the factor is focal length.

Answer 2

Unit of power of Lens is Dioptre

Explanation:

(a) The power of a lens is defined as a measurement of the degree of convergence or divergence of light rays falling upon it or reciprocal of the focal length of a lens

or Power, (P) = $\frac {1}{Focal Length}$

Hence, Power of a lens inversely proportional to the focal length.

(b) The Power has a unit dioptre (D) for the lens.  

1 Dioptre = Power of Lens for 1 m Focal Length.

(c) In case of I-Converging lens,

Focal length $(f_1)$ = 20 cm = 0.2 m

    For II-Converging lens,

Focal length $(f_2)$  = 40 cm = 0.4 m

    For Diverging Lens,

Focal length $(f_3)$ = - 50 cm = - 0.5 m (Due to sign convention = Negative Sign)

But Power, (P) = $\frac {1}{Focal Length}$

Power $(P_1)$ of 1st lens = $\frac {1}{0.2}$ = 5 D

Power $(P_2)$ of 2nd lens = $\frac {1}{0.4}$ = 2.5 D

Power $(P_3)$ of diverging  lens = $\frac {1}{-0.5}$ = - 2 D

Net power of the combination = $P_1 + P_2+ P_3 = 5 + 2.5 + (-2)$ = 5.5 D

• Net focal length of the combination = $\frac {1}{net\ power}$

= $\frac {1}{5.5}$

= 0.1818 m = 18.18 cm