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Question

# (a) What is myopia? (b) What are the causes of myopia? (c) Draw three labelled ray-diagrams to show the defect of vision called myopia and how it is corrected by the use of lenses. ​(d) The far point of a myopic person is 80 cm in front of the eye. What is the nature and power of the lens required to correct the defect?

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Solution

## (a) Myopia or short-sightedness is a common defect of vision in which a person is unable to see the farther objects but the nearby objects are clearly visible to him. (b) Myopia occurs when the eyeball is too long or the focal length of the eye lens is too short to focus the image on the retina. (c) (d) To correct the myopic eye, a concave lens is required. Far point of the myopic eye, v = 80 cm Object distance = $\infty$ Using lens formula, $\frac{1}{-80}-\frac{1}{\infty }=\frac{1}{f}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}⇒\frac{1}{f}=\frac{1}{-80}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}⇒f=-80\mathrm{cm}$ Therefore, the focal length of required to correct the defect is $-$80 cm. As the focal length is negative, so the lens is a concave lens. Power of the lens = $P=\frac{1}{-80×{10}^{-2}\mathrm{m}}=-\frac{100}{80}=-1.25\mathrm{D}$

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