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Edexcel GCSE Physics · 1PH0
Edexcel 1PH0 · 5.4P Check the specification (PDF) (opens in a new tab)
A lens forms an image by . Light changes direction at each curved boundary as it passes from air into the lens and then back into air. The directions of these changes combine to make rays converge towards the principal axis or diverge away from it.
A converging lens, often called a convex lens, is normally thicker in the centre. It brings rays arriving parallel to the principal axis together at the principal focus on the far side of the lens. A diverging lens, often called a concave lens, is normally thinner in the centre. It spreads parallel rays out; when those rays are traced backwards, they appear to come from a principal focus on the same side as the incoming light.
The focal length, , is the distance from the centre of the lens to its principal focus. A lens that changes the direction of light strongly brings rays together—or spreads them out—over a shorter distance, so it has a shorter focal length. A weak lens produces a smaller change in direction and has a longer focal length.
For lenses of the same material, greater curvature bends light more strongly. The principal focus is closer to the lens, so the focal length is shorter and the lens power is greater.
The power of a lens describes how strongly it focuses light. It is related to focal length by
Here, is the lens power in dioptres (D) and must be in metres (m). The dioptre is therefore equivalent to a reciprocal metre, .
Because power is the reciprocal of focal length, a shorter focal length means a greater magnitude of power. If the focal length is halved, the magnitude of the power doubles. Conversely, a long-focal-length lens has a small power and bends rays less strongly.
Lens power is not the same quantity as power measured in watts. Watts describe the rate of energy transfer; dioptres describe the focusing strength of a lens.
For lenses made from the same material, more strongly curved surfaces refract rays through larger angles. A more curved converging lens therefore brings parallel rays to a focus closer to the lens: its focal length is shorter and its power is greater. A flatter converging lens bends the rays less, so its focal length is longer and its power is smaller.
The same idea applies to diverging lenses. Greater curvature makes the rays spread out more strongly, so the apparent focus is closer to the lens and the magnitude of its power is greater.
Under the usual sign convention, a converging lens has a positive focal length and positive power. A diverging lens has a negative focal length and therefore negative power. Thus a large negative power describes strong divergence, while a large positive power describes strong convergence. When comparing how strongly lenses act, compare the magnitude of their powers as well as noticing the sign.
For the same lens material:
The sign shows whether the lens converges or diverges light; shows how strongly it does so.
Convert focal length to metres before using ; using centimetres gives the wrong numerical power.
Do not confuse lens power in dioptres (D) with power as a rate of energy transfer in watts (W).
When explaining shape, link the full chain: greater curvature causes stronger refraction, giving a shorter focal length and therefore a greater magnitude of lens power.
A diverging lens has a negative focal length and negative power under the usual sign convention.
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Lens
A transparent optical component that forms an image by refracting light at its surfaces.
Converging lens
A lens that refracts parallel rays so that they meet at the principal focus; it is usually thicker at the centre than at the edges.
Diverging lens
A lens that refracts parallel rays so that they spread out and appear to come from the principal focus; it is usually thinner at the centre than at the edges.
Principal focus
The point at which rays initially parallel to the principal axis meet, or appear to have come from, after passing through a lens.
Focal length
The distance from the centre of a lens to its principal focus, represented by and measured in metres when calculating lens power.
Lens power
A measure of how strongly a lens converges or diverges light, equal to the reciprocal of its focal length in metres.
Dioptre
The unit of lens power, symbol D; one dioptre is one reciprocal metre.
Put your knowledge into practice — try past paper questions for Physics
Lens
A transparent optical component that forms an image by refracting light at its surfaces.
Converging lens
A lens that refracts parallel rays so that they meet at the principal focus; it is usually thicker at the centre than at the edges.
Diverging lens
A lens that refracts parallel rays so that they spread out and appear to come from the principal focus; it is usually thinner at the centre than at the edges.
Principal focus
The point at which rays initially parallel to the principal axis meet, or appear to have come from, after passing through a lens.
Focal length
The distance from the centre of a lens to its principal focus, represented by and measured in metres when calculating lens power.
Lens power
A measure of how strongly a lens converges or diverges light, equal to the reciprocal of its focal length in metres.
Dioptre
The unit of lens power, symbol D; one dioptre is one reciprocal metre.