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Question
A person having short-sight cannot see objects clearly beyond a distance of 1.5 m. What would be the nature and power of the corrective lens to restore proper vision?
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Solution
A person suffering from short-sightedness can correct the defect by wearing spectacles fitted with concave lens. In order to find the power of the concave lens, we have to first calculate its focal length.
Given, the far point of the short-sighted person is 1.5 m from the eye (the person can see the object kept at infinity if the image of the object is formed at the person's own far point of 1.5 m from the eye).
`u=oo("the distance of the object")`
`v=-1.5m("far point of the defective eye in front of thhe lens ")`
`f=? ("focal length")`
The focal length can be calculated using the lens formula `1/f=1/v-1/u`
Substituting the values in the formula, we get
`1/-1.5-1/oo=1/f`
f=-1.5m,
Since,` 1/oo=0`
Now, that we know the focal length of the concave lens, its power can be calculated.
Power `P=1/(f) ("fin metres")`
∴ `P=-1/1.5=-0.667 Dioptres ~~-0.67 "Dioptres"`
Hence, the power of the concave lens required to rectify the defect is -0.67 D.
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