Question

A person can see clearly objects only when they lie between 50 cm and 400 cm from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use, will be :
A. Convex, +2.25 dioptre
B. Concave, -0.25 dioptre
C. Concave, -0.2 dioptre
D. Convex, +0.15 dioptre

Answer 1

Hint: Taking v = maximum possible distance the person should see an object in these types of questions and taking u as -6 and use the mirror formula i.e. $\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}$ and then use the power formula i.e. $P = \dfrac{1}{f}$ to determine the type and power of lens correction.
Used formula: Mirror formula $\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}$and power formula $P = \dfrac{1}{f}$

Complete Step-by-Step solution:
According to the given information v = -400cm = -4m and u = $ - \infty $
Using the mirror formula i.e. $\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}$ to find the focal length of lens
$ \Rightarrow $ $\dfrac{1}{f} = \dfrac{1}{{ - 4}} - \dfrac{1}{\infty }$
$ \Rightarrow $ $\dfrac{1}{f} = - \dfrac{1}{4}$
$ \Rightarrow $ f = -4m
Power of required lens $P = \dfrac{1}{f}$
Putting the value of f in formula
Therefore $P = \dfrac{1}{{ - 4}}$= -0.25D
Since the power is negative therefore the required lens is a concave lens.
Hence, the required lens needs to be a concave lens with power -0.25 dioptre.

Note: Power is the term in the above conversation which appears to be very interesting.In Ray Optics the power of a lens is its ability to bend light.The more power a lens has, the greater its ability to refract light that goes through it.For a convex lens, the ability to converge is determined by power, and the ability to diverge in a concave lens.