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Question
An eye has a far point of 2 m. What type of lens in spectacles would be needed to increase the far point to infinity? Also calculate the power of lens required. Is this eye long-sighted or short-sighted?
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Solution
The far point of an eye can be increased by wearing spectacles with concave lens. In order to find the power of the concave lens required, we have to first calculate its focal length.
Given that the far point of the short-sighted person is 2 m in front of the eye (the person can see objects kept at infinity if the images of the objects are formed at the person's own far point of 2 m from the eye).
`u=oo("the distance of the object")`
`v=-2m("the far point of the defective using the formula ")1/f=1/v-1/u`
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/-2-1/oo=(-1)/2 ("Sinc e, 1/oo=0")`
∴ f=-2 m
Now that we know the focal length of the concave lens required, its power can be calculated.
Power `P=1/f` (for f in meters)
∴` P=1/-2=-0.5 D`
Hence, the power of the concave lens required to rectify the defect is -0.5 D.
This eye is short-sighted.
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