Question

Power of a lens is a measure of the ability of the lens to converge the rays of light falling on it. Quantitatively, power of a lens = reciprocal of focal length of lens, i.e., `P=(1)/(f)`. If a lens happens to diverge the ray of light falling on it, its power is said to be negative. Thus, power of a convex lens is positive and power of a concave lens is negative.
If `P_1,P_2` are powers of two lenses held in contact with each other, the power of the combination is `P=P_1+P_2`. Note that `P_1,P_2` are to be added with proper sign.
Read the above passage and answer the following question:
(i) What is the SI unit of power?
(ii) Focal length of a concave lens is `20 cm`. What is its power ?
(iii) What lessons of life do you learn from the relation `P=P_1+P_2`?

Answer 1

(i) SI unit of power is diopter (D). One diopter is the power of lens of focal length one meter.
(ii) Here, `f =- 20 cm = -20/100 m= -1/5m. P=(1)/(f)=(1)/(-1//5) = -5D`
(iii) If `P_1=3D` and `P_2 = - 2D` then
`P=P_1+P_2=3D-2D=1 D`
Again, if `P_1=3 D` and `P_2 = 2 D`, then
`P = P_1 + P_2 = 3D +2D = 5D`
i.e., power of combination is much larger when the two lenses are of same nature. The same is true in real life. To make a powerful combination in business, partners should preferably be of same nature. Same is true for life partners, i.e., husband and wife. If their nature is identical, they will make an adorable couple.