Lenses — Quick Summary

Mr Toogood's Physics · Astrophysics

AQA 3.9.1.1
1/f = 1/u + 1/v
Lens equation
M = v/u = hᵢ/hₒ
Magnification
Power = 1/f
Dioptres (m⁻¹)
+ real, − virtual
Sign convention

Refraction & focusing

Parallel rays refracted by a convex lens and brought to a single focus

Rays further from the axis are refracted more, bringing parallel rays to one focus.

Lenses use refraction to bend light. A curved lens refracts rays by different amounts depending on their distance from the axis, so parallel incident rays converge at a single principal focus (unlike a flat block, which just displaces rays).

Key terms

Diagram labelling the principal axis, principal focus, focal length and focal plane of a lens

Principal axis, principal focus, focal length (f), focal plane.

Three standard rays

  • Through the centre of the lens — undeviated.
  • Parallel to the axis — refracts through the focal point.
  • Through the focal point (objective side) — emerges parallel to the axis.

Draw any two of these from the same point on the object; where they cross (image side) locates the image.

Object-distance cases

Object atNatureOrient.SizeUse
> 2FRealInvertedDiminishedCamera
= 2FRealInvertedSame size—
1F–2FRealInvertedMagnifiedProjector
= 1FReal (∞)InvertedN/ASearchlight
< 1FVirtualUprightMagnifiedMagnifying glass

The lens equation

Ray diagram with similar triangles used to derive the lens equation and magnification

Similar triangles on both sides of the lens link u, v, f, and the heights.

Comparing similar triangles on the object and image sides gives both the magnification and the lens equation:

M = v/u = hᵢ/hₒ     1/f = 1/u + 1/v
Reading the sign: positive values are real; a negative value (commonly for v) indicates a virtual image. Power (1/f) is measured in dioptres, m⁻¹.

Exam essentials

Key equations

  • 1/f=1/u+1/v
  • M=v/u=hᵢ/hₒ

Sign convention

  • Real image/distance → positive.
  • Virtual image/distance → negative.
  • Power in dioptres = 1/f (f in metres).

Common slips

  • Convert cm → m before calculating power in dioptres.
  • The equation won't tell you orientation — memorise: a real image from a convex lens is always inverted.
  • Identify which object-distance case applies before assuming image properties.