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(a) A person can see clearly upto 80 cm....

(a) A person can see clearly upto `80 cm`. He uses spectacles of `-0.80 dioptre`, how far can he see clearly ?
(b) If a person uses spectacles of power `+ 1.0 dioptre`, what is the nearest distance of distinct vision for him ? Given that near point of the person is `75 cm` from the eye.

Text Solution

Verified by Experts

(a) Here, `P = - 0.80 dioptre`
`f = (100)/(P) = (100)/(-0.8) = - 125 cm`
`v = - 80 cm, u = ?`
As `(1)/(v) - (1)/(u) = (1)/(f)`
`:. (1)/(u) = (1)/(v) - (1)/(f) = (1)/(-80) + (1)/(125)`
`= (-25 + 16)/(2000) = (-9)/(2000)`
`u = - (2000)/(9) = - 222.22 cm`
The person can see objects upto `222.22 cm`.
(b) Here, `P = 1.0 dioptre`
`f = (100)/(P) = (100)/(1) = 100 cm`
`u = ? v = - 80 cm`,
As `(1)/(v) - (1)/(u) = (1)/(f)`
`:. (1)/(u) = (1)/(v) - (1)/(f) = -(1)/(75) - (1)/(100) = (-4 - 3)/(300)`
`u = -(300)/(7) = - 42.9 cm`.
`:.` The nearest distance of distinct vision of the person is `42.9 cm`
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