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 diopter
B.
concave, - 0.25 diopter
C.
concave - 0.2 diopter
D.
convex, + 0.15 diopter
Answer :
concave, - 0.25 diopter
Solution :
Image of object at $$\infty $$ must lie within distance upto which person can view clearly.
Image distance, $$v = 400\,cm = 4\,m \Rightarrow u = \infty $$
Using lens equation, $$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$
$$\eqalign{
& \Rightarrow \frac{1}{{ - 4}} - \frac{1}{\infty } = \frac{1}{f} \cr
& \Rightarrow f = - 4\,m \cr} $$
Now power of the required lens is,
$$P = \frac{1}{f} = \frac{1}{{ - 4}} = - 0.25D$$
Thus, the person require a concave lens of power $$ - 0.25D.$$