The dioptre
The unit of lens power, and what its sign means.
An optician's prescription
An optician writes a number such as +2.0 D on a prescription for glasses. That number tells the kind of lens and its focal length.
What does a positive number on such a prescription tell you?
What this lesson covers
The idea
The SI unit of lens power is the dioptre (D): 1 D = 1 m⁻¹, the power of a lens of focal length 1 m, with f in metres; convex lenses have positive and concave lenses negative power.
An optician's prescription
An optician writes a number such as +2.0 D on a prescription for glasses. That number tells the kind of lens and its focal length.
What does a positive number on such a prescription tell you?
- The lens is convex
- The lens is concave
- The lens is flat glass
Match the lens
Tap a power on the left, then the lens it describes on the right. Divide 1 by the power to get f in metres.
Powers and signs
A power of +2.0 D means f = 1/2.0 = 0.50 m, a convex lens. A power of −2.5 D means f = 1/(−2.5) = −0.40 m, a concave lens.
The SI unit of lens power is the dioptre (D). If f is in metres, the power is in dioptres. 1 D = 1 m⁻¹, the power of a lens whose focal length is 1 metre. The power of a convex lens is positive and that of a concave lens is negative.
Notes
Unit of power: the dioptre (D). 1 D = 1 m⁻¹, the power of a lens of focal length 1 m (f in metres). Convex: positive power. Concave: negative power.
Check yourself
What is 1 dioptre?
A lens has a focal length of +0.50 m. What is its power, in dioptres?
Answer: 2 D
P = 1/f = 1/0.50 = +2 D. A positive power means the lens is convex.
An optician prescribes a lens of power −2.5 D. What is its focal length, in metres?
Answer: -0.4 m
f = 1/P = 1/(−2.5) = −0.40 m. The lens is concave.
A lens has power −2.5 D. What kind of lens is it?
- The power of a lens whose focal length is 1 centimetre. One dioptre is for f = 1 metre. A focal length of 1 cm is 0.01 m, and the power would be 100 D.
- The power of a lens whose focal length is 1 metre — correct. Yes!
- The power of a lens whose focal length is 1 dioptre. Dioptre is a unit of power, not of focal length. Focal length is measured in metres.
- A convex lens. The power of a convex lens is positive.
- It cannot be told from the power. The sign of the power tells the kind of lens: positive for convex, negative for concave.
- A concave lens — correct. Yes!