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A myopic person can clearly see objects only up to 4 m and wants to see objects up to 20 m. Using $f = \dfrac{xy}{x-y}$, what focal length concave lens is needed?
A$-2\ \text{m}$
B$-16\ \text{m}$
C$-5\ \text{m}$
D$+5\ \text{m}$
Answer & Solution
Correct answer: C. $-5\ \text{m}$
1. Use $f = \dfrac{xy}{x-y}$ with $x = 4$ m and $y = 20$ m.
2. Numerator: $xy = 4 \times 20 = 80$.
3. Denominator: $x - y = 4 - 20 = -16$.
4. So $f = \dfrac{80}{-16} = -5$ m.
5. The negative sign confirms a concave lens is required for myopia.
6. A positive value would imply a convex lens, which is the wrong defect, so $+5$ m is a trap.
_Source: Samacheer Kalvi (TN SCERT) Class 10 Science, Unit 2 Optics "Solved Problems", p.35_
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