Lens power increases as focal length decreases
Definition
Principal focus
The point on the principal axis at which rays parallel to the axis converge, or appear to diverge from, after passing through a lens.
Definition
Focal length
The distance from the optical centre of a lens to its principal focus.
- The principal axis is the straight line through the optical centre and both principal foci.
- The optical centre is the central point of a thin lens through which a ray passes without changing direction.
- The power of a lens measures how strongly it converges or diverges light.
- Lens power is calculated using P=1fP=\dfrac{1}{f}P=f1, where PPP is in dioptres, D\text{D}D, and fff is in metres, m\text{m}m.
- A shorter focal length gives a larger magnitude of power because the rays are bent more strongly.
- A converging lens has positive power, while a diverging lens has negative power.
Example
Calculating lens power
- A converging lens has focal length 20 cm=0.20 m20\ \text{cm}=0.20\ \text{m}20 cm=0.20 m.
- Using P=1fP=\dfrac{1}{f}P=f1 gives P=10.20=+5.0 DP=\dfrac{1}{0.20}=+5.0\ \text{D}P=0.201=+5.0 D.
- A diverging lens with focal length −0.50 m-0.50\ \text{m}−0.50 m has power P=1−0.50=−2.0 DP=\dfrac{1}{-0.50}=-2.0\ \text{D}P=−0.501=−2.0 D.
Shape determines how strongly a lens bends light
Definition
Converging lens
A lens that is thicker at the centre than at the edges and refracts parallel rays towards a principal focus.
Definition
Diverging lens
A lens that is thinner at the centre than at the edges and refracts parallel rays so that they spread out as if they came from a principal focus.
- A more strongly curved converging lens changes the direction of rays more, so it has a shorter focal length and a larger positive power.
- A less strongly curved converging lens bends rays less, so it has a longer focal length and a smaller positive power.
- A more strongly curved diverging lens spreads rays more, so the magnitude of its negative power is larger and its focal length has a smaller magnitude.
- Lens material also affects refraction, but comparisons of shape assume the same transparent material.
Power must be compared using magnitude and sign
- The sign identifies the type of lens: positive for converging and negative for diverging.
- The magnitude, ∣P∣|P|∣P∣, identifies the strength of the lens.
- A lens of −6 D-6\ \text{D}−6 D is stronger than a lens of +2 D+2\ \text{D}+2 D because 6>26>26>2, although the lenses bend rays in opposite ways.
Common Mistake
- Convert centimetres to metres before using P=1fP=\dfrac{1}{f}P=f1.
- Do not say that a larger focal length means a more powerful lens; power is inversely proportional to focal length.
- Do not ignore the sign of the power when identifying whether a lens converges or diverges light.
Exam technique
Power calculations
- Write P=1fP=\dfrac{1}{f}P=f1 and convert the focal length to metres before substitution.
- Include the unit D\text{D}D and use the sign to identify the lens type.
- When comparing lens strength, compare ∣P∣|P|∣P∣ rather than only the signed numerical values.
Self review
- Define focal length.
- State the equation linking lens power and focal length.
- Explain why a more strongly curved converging lens has greater power.
- State the sign of the power of a diverging lens.
- Calculate the power of a converging lens with focal length 0.25 m0.25\ \text{m}0.25 m.
