A Prescription of −0.50 D
A 15-year-old student in Patna cannot read the blackboard beyond about 2 m, although she reads a book held at 25 cm without difficulty. An optician trial-fits a concave lens of power −0.50 D and she can see distant objects clearly. The prescription is written as 'distance vision only'. She spends about six hours a day on a smartphone held roughly 20 cm from her face. Her father has a spare convex lens labelled +2.50 D and asks whether it can be used instead, since 'both are lenses and the power is even higher'. The student also reports that after two hours of reading under a dim bulb her eyes ache and the print blurs, and she has heard that wearing glasses continuously will increase her power. The family wants a clear explanation of what is happening before they buy the glasses.
1. Name the defect, calculate the focal length of the prescribed lens, and explain in words why the unaided image of a distant object does not fall on the retina.
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The defect is myopia, or short-sightedness. The prescribed lens has P = −0.50 D, so f = 1/P = 1/(−0.50) = −2.0 m. The negative sign means a concave, diverging lens.
In an unaided myopic eye, the eye lens is too strong for the length of the eyeball, or the eyeball is too long. Parallel rays from a distant object converge in front of the retina, so the image on the retina is blurred. The far point is only about 2 m away.
The concave lens diverges the incoming parallel rays slightly before they enter the eye. The eye lens then converges them farther back, so the final image forms on the retina. The lens does not 'cure' the eye; it compensates for the refractive error.
2. The father suggests using the +2.50 D convex lens instead. Use the lens formula or ray reasoning to show why this is not a harmless substitution.
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The +2.50 D lens has f = 1/(+2.50) = +0.40 m. It is a converging lens, appropriate for hypermetropia, not myopia.
A converging lens makes rays from a distant object converge even earlier. In a myopic eye that already focuses parallel rays in front of the retina, adding a convex lens moves the image even farther forward and makes the blur worse. The eye cannot compensate because the rays have already been bent inward before reaching the eye lens.
So the two lenses are not interchangeable. The sign of the power is as important as the number. Using the father's lens would cause headache and blurred distance vision, and it should not be tried as a substitute.
3. Explain the eye ache and blur after long dim-light reading. Does wearing the correct glasses continuously weaken the eyes or increase the power? What practical advice would you give?
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In dim light the pupil dilates to let in more light, which increases optical aberrations and reduces depth of focus. The ciliary muscle must sustain accommodation for close work, and staring at a phone reduces blinking, drying the tear film. The ache is muscle and tear-film fatigue, not evidence that the retina is being damaged.
Correct glasses do not weaken the eyes and do not increase the power. Myopia often progresses during the teenage growth years because the eyeball elongates; that progression is not caused by wearing glasses.
Practical advice: use the −0.50 D glasses for distance vision as prescribed, hold the phone farther away (about 30–40 cm), read in adequate light, follow the 20-20-20 rule (every 20 minutes look 20 feet away for 20 seconds), and spend some time outdoors. Regular eye checks are more useful than avoiding glasses.