Question:
An optician prescribes a corrective lens of power +2D, then the focal length of the required convex lens is
An optician prescribes a corrective lens of power +2D, then the focal length of the required convex lens is
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Power of a lens (in Diopters, D) is $P = 1/f$, where $f$ is the focal length in meters.
A positive power indicates a convex (converging) lens.
A negative power indicates a concave (diverging) lens.
To convert meters to centimeters, multiply by 100.
Updated On: May 26, 2025
- 10 cm
- 50 cm
- 10 m
- 50 m
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The Correct Option is B
Solution and Explanation
The power ($P$) of a lens is the reciprocal of its focal length ($f$) in meters.
$P = \frac{1}{f(\text{in meters})}$.
Given the power $P = +2D$ (Diopters).
The positive sign indicates that it is a convex lens (converging lens).
We need to find the focal length $f$.
From the formula, $f(\text{in meters}) = \frac{1}{P}$.
$f = \frac{1}{+2D} = 0.5 \text{ meters}$.
The options are given in centimeters and meters. Let's convert our answer to centimeters.
$1 \text{ meter} = 100 \text{ centimeters}$.
$f = 0.5 \text{ m} \times 100 \frac{\text{cm}}{\text{m}} = 50 \text{ cm}$.
This matches option (b).
\[ \boxed{50 \text{ cm}} \]
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