a short sighted person can read book situated at a distance of 15 cm what should be the focal length and nature of lens so that the person can read a book kept at 25 CM
Answers
A short-sighted person can see clearly at a distance of 15 cm. What lens is required for him in order to be able to see an object clearly at 60 cm?
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3 Answers
Victor Mazmanian, former Associate Prof. Of Physics (Retired) at United States Air Force Academy
Answered May 29, 2018 · Author has 1.5K answers and 2M answer views
The question is poorly worded. We must infer some facts from a poorly written question in order to answer the question properly. I am using the following inferences:
(1) Because we are told that the myopic person can see clearly at 15 cm, we can deduce that the NEAR POINT of the eye is 15 cm as opposed to the NORMAL NP of 25 cm.
(2) We are not told the Far Point of this eye. It cannot be infinity (the FP of a normal eye) because, as established in (1), the eye is myopic. So it must be LESS than infinity. The eye charts that we use consider infinity for a normal eye to be 600 cm (20 feet) where the fifth/sixth line of the chart could be readily read by the observer.
(3) Since we are not told the FP of this eye, we cannot take the eye as being UNABLE to see clearly at 60 cm. It may or it may not. Therefore I think the question should be reworded to ask: where would the image of an object at 60 cm be, using the correcting lens.
Solution: Do = 25 cm (the NP of a normal eye).
Di = - 15 cm (the NP pf the defective eye).
1/f = 1/25 - 1/15 → f = - 37.5 cm. This lens is a DIVERGING (concave) lens, since the focal length is negative, and it checks with the fact that myopia corrective lenses are diverging.
Using the newly found (f) we can obtain the final answer: -1/37.5 = 1/60 + 1/Di → Di = - 23.1 cm. This is a reasonable answer, because images provided by concave lenses are virtual, and a negative Di is virtual by convention.
The following image illustrates the above phenomenon (courtesy of the physics classroom):
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