CAPF AC 2022 Q25: Science & Technology – Physics
The magnitude of focal length of a concave lens is 2 m. What is the power of the lens?
- (a) +0.5 dioptre
- (b) -0.5 dioptre
- (c) +2.0 dioptre
- (d) -1.0 dioptre
Answer: (b) -0.5 dioptre
Explanation
Power of a concave lens
Given: the magnitude of the focal length of a concave lens is 2 m; find its power.
How to think: power is the reciprocal of the focal length in metres.
The sign depends on the lens.
A concave (diverging) lens has a negative focal length.
| Step | Working |
|---|---|
| Focal length with sign | f = −2 m |
| Formula | P = 1/f |
| Power | P = 1/(−2) = −0.5 dioptre |
Sign rule: convex lens → positive power.
Concave lens → negative power.
Answer: (b) −0.5 dioptre.
Why each option is right or wrong
- (a) Incorrect. +0.5 dioptre would be a convex lens of focal length 2 m.
- (b) CORRECT. P = 1/(−2 m) = −0.5 dioptre.
- (c) Incorrect. +2.0 dioptre comes from using the focal length itself, with the wrong sign.
- (d) Incorrect. −1.0 dioptre would be a concave lens of focal length 1 m.
Key point
P = 1/f (f in metres); unit dioptre (D). Convex lens: positive power, corrects long-sightedness. Concave lens: negative power, corrects short-sightedness. Powers of lenses in contact add up.
Remember
P = 1/f in metres; concave lens is negative.
Common mistakes
- Forgetting the negative sign for a concave lens.
- Writing the power as 2 dioptre instead of taking the reciprocal.
- Using centimetres instead of metres for the focal length.
Exam tip
Educated guess: concave means minus, which removes (a) and (c). The reciprocal of 2 is a half, which gives (b).
Sources
- NCERT Class X Science — Light: Reflection and Refraction (power of a lens)
- NCERT Class XII Physics — Ray Optics and Optical Instruments