Question

# A person cannot see distinctly objects kept beyond$2m$. This defect can be corrected by using a lens of power

A

+ 0.5 D

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B

– 0.5 D

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C

+ 0.2 D

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D

– 0.2 D

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Solution

## The correct option is B – 0.5 DStep (1): Given:The far point of the person, $D=2m$This means the person cannot see the objects situated beyond 2 m from the eye.Step (2): Statement of Myopia:Short-sightedness is an eye defect that causes the person to see far away objects as blurry or out of focus. The scientific term in use for short-sightedness is myopia.From the given situation, the person is suffering from short-sightedness (or) myopia. A concave lens is used to correct myopia.The far point of the given myopic eye, D is at 2 m.Step (3): Finding the focal length of the lens:Let the object distance $u=-\infty$and image distance (v) = distance of far point = -DLet 'f' be the focal length of the bi-concave lens.Using the lens formula,$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$$\frac{1}{f}=\frac{1}{\infty }-\frac{1}{2}\phantom{\rule{0ex}{0ex}}\frac{1}{f}=-\frac{1}{2}\phantom{\rule{0ex}{0ex}}\therefore f=-2m$Step (4): Finding the power of the lens:We know that the required power of the lens, $P=\frac{1}{f}\phantom{\rule{0ex}{0ex}}Bysubstitutingthegivenvalue,weget\phantom{\rule{0ex}{0ex}}P=\frac{1}{-2}\phantom{\rule{0ex}{0ex}}=-0.5D$A concave lens of power of -0.5 D is required to fix the myopic eye.Hence, the correct answer is (B) – 0.5 D

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