What is the unit of measurement for optical power of the lens?

Correct — D. The diopter, in the paper's spelling, is the unit of the power of a lens, defined as P = 1/f with the focal length f measured in metres.

One diopter is the power of a lens of focal length one metre, so the unit is m⁻¹.

A converging lens has positive power and a diverging lens negative power, and a shorter focal length means a stronger lens — option (d).

Why the others are wrong

• (a)
  Katal — The katal is the SI unit of catalytic activity, one mole of substrate converted per second. It belongs to biochemistry and has nothing to do with optics.
• (b)
  Yotta — Yotta is not a unit at all. It is the SI prefix for 10²⁴, used in front of a unit, as in yottabyte.
• (c)
  Radian — The radian is the SI unit of plane angle, the angle subtending an arc equal to the radius. Optics uses it for angles, never for the power of a lens.

The power of a lens says how strongly it bends light, and it is the reciprocal of the focal length in metres: P = 1/f.

The resulting unit m⁻¹ is given the name diopter (D). A convex lens of focal length 50 cm has P = 1/0.5 = +2 D, and a concave lens of the same focal length has −2 D.

Powers add, so two thin lenses in contact behave as a single lens of power P₁ + P₂. That is why spectacle prescriptions are written in diopters.

Key facts

• The power of a lens is P = 1/f, with f in metres.
• The unit of lens power is the diopter, equal to m⁻¹.
• Convex lenses have positive power and concave lenses negative power.
• The katal is the SI unit of catalytic activity and the radian the SI unit of plane angle.

Common traps

• Answering radian because it is the only familiar SI unit in the list.
• Forgetting to convert the focal length to metres, which turns 20 cm into 5 D and not 0.05 D.

No directly related past PYQ was found.