Question

S. I. unit of power of lens is :

• A. Diopter
• B. Decibel
• C. Meter
• D. Gauss

Hint:

The power of a lens (\(P\)) is \(1/f\), where \(f\) is the focal length. The SI unit of power is the Diopter (D). Crucially, to calculate power in Diopters, the focal length \(f\) must be in meters. For example, a lens with a focal length of 50 cm (0.5 m) has a power of \(1/0.5 = +2 \text{ D}\) (if converging).

Answer 1

The Correct Option is A

Concept: The power of a lens is a measure of its ability to converge or diverge light. It is defined as the reciprocal of its focal length. Step 1: Define the power of a lens The power (\(P\)) of a lens is given by the formula: \[ P = \frac{1}{f} \] where \(f\) is the focal length of the lens. Step 2: SI unit of focal length The focal length (\(f\)) is a distance. The SI unit of distance is the meter (m). For the power of a lens to be expressed in its standard unit (Diopter), the focal length \(f\) must be expressed in meters. Step 3: Determine the SI unit of power If \(f\) is in meters (m), then the unit of power \(P\) would be \(\text{m}^{-1}\) (reciprocal meter or per meter). This unit, \(\text{m}^{-1}\), is specifically named the Diopter (D). So, \(1 \ \text{Diopter (D)} = 1 \ \text{m}^{-1}\). Step 4: Evaluate the given options
(1) Diopter: This is the correct SI unit for the power of a lens.
(2) Decibel (dB): This is a logarithmic unit used to express ratios, commonly for sound level or signal power in electronics. It is not the unit for the power of a lens.
(3) Meter (m): This is the SI unit of length (and focal length), not power of a lens.
(4) Gauss (G): This is a unit of magnetic flux density (magnetic field strength) in the CGS system. It is not related to the power of a lens. Therefore, the S.I. unit of power of lens is Diopter.