Dr. Meena, an ophthalmologist, is conducting vision screening at a school. She tests four students: Arjun (age 12) can read the blackboard clearly from the back row but struggles to read his textbook held at 25 cm; his near point has shifted to 45 cm. Bela (age 14) can read her textbook easily but cannot read the blackboard from the back row; her far point is only 2 m away. Chetan (age 13) has been prescribed lenses of power +2.5 D for one eye and −1.5 D for the other. Deepa (age 70) can neither read her phone clearly nor see distant objects sharply without her bifocal glasses.
Read the following passage and answer the questions that follow.
Dr. Meena, an ophthalmologist, is conducting vision screening at a school. She tests four students:
• Arjun (age 12) can read the blackboard clearly from the back row but struggles to read his textbook held at 25 cm. His near point has shifted to 45 cm.
• Bela (age 14) can read her textbook easily but cannot read the blackboard from the back row. Her far point is only 2 m away.
• Chetan (age 13) has been prescribed lenses of power +2.5 D for one eye and −1.5 D for the other.
• Deepa (age 70, a teacher accompanying the group) tells Dr. Meena that she can neither read her phone clearly nor see distant objects sharply without her bifocal glasses.
(a) Identify the defect of vision that Arjun has, and name the type of lens Dr. Meena will prescribe for him.
(b) What is the far point of a normal eye? Using this information, calculate the focal length of the corrective lens required by Bela.
(c) State the defect Deepa suffers from. Explain TWO reasons why this defect develops, and state the type of lens used in the UPPER and LOWER halves of her bifocal glasses.
OR
(c) The two eyes of Chetan have been prescribed lenses of power +2.5 D and −1.5 D respectively. Name the defect in each eye and calculate the focal length of each corrective lens. State what property of lenses allows the doctor to simply add their powers when combining lenses.
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Dr. Meena will prescribe a CONVEX (converging) lens.
[1 mark: defect identified correctly + correct lens named]
(b) The far point of a NORMAL eye is at INFINITY.
For Bela, the corrective lens must form a virtual image of a distant object (at infinity) at her far point of 2 m, so that her eye can then form a clear image on the retina.
Using the lens formula: 1/v − 1/u = 1/f
Here, object is at infinity: u = −∞
Image must be formed at Bela's far point: v = −2 m (virtual image, on same side as object)
⟹ 1/f = 1/v − 1/u = 1/(−2) − 1/(−∞)
⟹ 1/f = −1/2 − 0
⟹ 1/f = −1/2
∴ f = −2 m = −200 cm
The focal length of the corrective lens required by Bela is −200 cm (i.e., −2 m).
(This is a concave/diverging lens, consistent with myopia correction.)
[1 mark: far point of normal eye stated as infinity + correct calculation with sign convention + answer with unit]
(c) Deepa suffers from PRESBYOPIA.
This defect develops due to the following TWO reasons:
(i) The ciliary muscles weaken with age, reducing their ability to change the curvature of the eye lens.
(ii) The crystalline lens of the eye loses its flexibility and becomes less elastic with age, so it can no longer adjust its focal length for near or far objects.
In Deepa's bifocal glasses:
— UPPER half: CONCAVE (diverging) lens — to correct the inability to see distant objects clearly.
— LOWER half: CONVEX (converging) lens — to correct the inability to see near objects clearly.
[2 marks: defect named (½) + both causes stated (½ each) + both halves of bifocal lens correctly identified (½)]
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OR (c)
Chetan's eye with +2.5 D lens:
Positive power → CONVEX lens → corrects HYPERMETROPIA (far-sightedness).
Focal length: f = 1/P = 1/+2.5 = +0.4 m = +40 cm
Chetan's eye with −1.5 D lens:
Negative power → CONCAVE lens → corrects MYOPIA (near-sightedness).
Focal length: f = 1/P = 1/(−1.5) = −0.67 m ≈ −67 cm
The property that allows the doctor to simply add the powers of lenses is:
"When two thin lenses are placed in contact, the effective power of the combination is equal to the algebraic sum of their individual powers."
i.e., P_total = P₁ + P₂
This holds because power (P = 1/f) is additive for lenses in contact, making it convenient for prescribing combined corrections.
[2 marks: both defects correctly named (½ each) + both focal lengths calculated correctly with units (½ each) + property of additive powers stated (½) — total adjusted to 2 marks]