3.10.1.2
Power of a lens and lens combinations
Medical Physics | AQA A-Level Physics
Key Definition
Power of a lens: The reciprocal of the focal length in metres. $P = \frac{1}{f}$. Measured in dioptresThe unit of lens power. 1 dioptre = 1 m⁻¹. A lens with focal length 0.5 m has power +2.0 D. (D), where 1 D = 1 m⁻¹.
- A converging lens has positive power. A diverging lens has negative power.
- A short focal length means a high power, meaning the lens refracts light more strongly.
- For thin lenses in contact, the combined power is simply the sum of the individual powers: $P_{\text{total}} = P_1 + P_2 + P_3 + \ldots$
- This is why opticians prescribe lenses by power in dioptres rather than focal length in metres.
Worked Example
A converging lens of power +4.0 D is placed in contact with a diverging lens of power -1.5 D. Calculate the combined focal length.
Show Solution
1
Add the powers
$$P_{\text{total}} = +4.0 + (-1.5) = +2.5 \text{ D}$$
2
Calculate the focal length
$$f = \frac{1}{P} = \frac{1}{2.5} = 0.40 \text{ m}$$
Answer
$f = 0.40$ m (converging, since $P$ is positive).