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Question
An eye has a near point distance of 0.75 m. What sort of lens in spectacles would be needed to reduce the near point distance to 0.25 m? Also calculate the power of lens required. Is this eye long-sighted or short-sighted?
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Solution
A person suffering from hypermetropia can correct the defect by wearing spectacles containing convex lenses. In order to find the power of the convex lens required, we have to first calculate its focal length.
Given that the near point of the hypermetropic person is 0.75 m from the eye (the person can see objects kept at the normal near point of 0.25 m in front of the eye if the images of the objects are formed at the person's own near point of 0.75 m from the eye).u=-0.25m(the distance of the object at the normal near point)v=-0.75m (the near point of the defective eye in front of the lens)
f = ? (focal length)
The focal length can be calculated using the formula `1/f=1/v-1/u`
Substituting the values in the formula, we get
`1/f=1/-0.75-1/-0.25`
`1/f=((-1+3)/0.75)`
∴f =2.67 m
Now that we know the focal length of the convex lens, its power can be calculated.
Poer `P=1/(f "in meters")`
Hence, the power of the convex lens required to rectify the defect is +0.37 D.
This eye is long-sighted.
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