A certain person can see clearly objects lying between `20 cm and 250 cm` from his eye. What spectacles are required to enable him to see distant objects clearly ? When he is wearing these spectacles, what is his least distance of distinct vision ?

Explanation

Here, distance of far point `x = 250 cm`. Therefore, to see distant objects clearly, he has to use concave lens of focal length
`f = -x = - 250 cm = - 2.5 m`
Power of this lens, `P = (1)/(f) = (1)/(- 2.5) = -0.4 D`
Now, distance of near point of defective eye, `x = 20 cm`
and let `d` be the distance of distinct vision when he is wearing spectacles.
From `(1)/(f) = (1)/(v) - (1)/(u) = (1)/(x) - (1)/(d) = (d - x)/(xd)` ltbegt `f = (xd)/(d - x) = (20 d)/(d - 20)`
`-250 = (20 d)/(d -20)`
`-250 d + 5000 = 20 d`
`270 d = 5000, d = (5000)/(270) = 18.51 cm`