A person needs a lens of power –4.5 D for correction of her vision.(a) What kind of defect in vision is she suffering from?(b) What is the focal length of the corrective lens?(c) What is the nature of the corrective lens?
Question
A person needs a lens of power –4.5 D for correction of her vision.(a) What kind of defect in vision is she suffering from?(b) What is the focal length of the corrective lens?(c) What is the nature of the corrective lens?
Solution
(a) The person is suffering from myopia or nearsightedness. This is indicated by the negative power of the lens.
(b) The power P of a lens is given by the formula P = 1/f, where f is the focal length of the lens. The focal length is measured in meters. So, to find the focal length, we rearrange the formula to f = 1/P. Substituting the given power of -4.5 D (or -4.5 diopters), we get f = 1/(-4.5 D) = -0.22 meters or -22 cm. The negative sign indicates that the focal length is on the opposite side of the lens from the light being focused.
(c) The nature of the corrective lens is diverging or concave. This is because a negative lens power corresponds to a lens that spreads out light rays, which is what a diverging or concave lens does. This type of lens is used to correct myopia by diverging the light rays before they reach the eye, which effectively moves the far point of the eye to the retina.
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