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The near and far points of a person are ...

The near and far points of a person are at `40 cm` and `250cm` respectively. Find the power of the lens he/she should use while reading at `25cm`. With this lens on the eye, what maximum distance is clearly visible?

Text Solution

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If an object is placd at 25 cm from the correcting lensl it should produce the virtual image at 40 cm. Thus, `u=-25cm, v=-40cm`
`1/f=1/v-1/u`
`=1/(40cm)+1/(25cm)`
or `f=200/3cm=+2/3m`
`P=1/f+1.5D`
The uN/Aided eye can see a maximum distance of 250 cm. Suppose the maximum distance for clear vision is d when the lens is used. Then the object at a distance d is imaged by the lens ast 250 cm. We have
`1/v-1/u=1/f`
`or - 1/(250cm)-1/d=3/(200cm)`
`or d=-53cm`
Thus the person will be able to see up to a maximum distance of 53 cm.
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