Power of a lens
- CBSE · NCERT Class 10, Ch 9 Light - Reflection and Refraction
The power of a lens is 1 divided by its focal length in metres, measured in dioptres, and shows how strongly the lens bends light.
P = 1/f. A lens with a short focal length bends light sharply, so its power is large. The SI unit is the dioptre, D. One dioptre is the power of a lens with a focal length of 1 metre, so 1 D = 1 m⁻¹.
The focal length must be in metres, not centimetres. A convex lens has positive power and a concave lens negative power. When lenses are placed in contact, their powers add: P = P1 + P2.
A small example
A convex lens of focal length 50 cm is placed against a concave lens of focal length 25 cm. First change both to metres, with their signs.
- P1 = 1/(+0.50 m) = +2 D.
- P2 = 1/(-0.25 m) = -4 D.
- P = +2 D + (-4 D) = -2 D.
- f = 1/P = 1/(-2 D) = -0.5 m, or -50 cm.
The power is negative, so the pair behaves like a concave lens.
Where marks go
A numerical can place a convex and a concave lens together. With step marking, each power and the sum can earn marks, so show each line of working.
Two details decide the numbers. The concave lens needs its minus sign. Each focal length needs changing to metres before dividing, or the answer is 100 times too small. Read why SI units matter in an answer.
Sources
Facts last checked against these sources on 30 September 2026.
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