The Thin-Lens Equation

A lens bends light rays so they meet again at a point, forming an image. Where that image forms depends on how far the object sits from the lens and how strongly the lens bends light, a property called its focal length. The thin-lens equation ties these three distances together, so knowing any two lets you find the third.

1/f = 1/dₒ + 1/dᵢ

  • f — focal length (m): how strongly the lens bends light — where parallel rays converge
  • dₒ — object distance (m): how far the object is from the lens
  • dᵢ — image distance (m): how far the image forms from the lens

A converging lens has a focal length of 10 cm. An object is placed 30 cm in front of it. How far from the lens does the image form?

  • f = 10 cm
  • dₒ = 30 cm
  1. 1/dᵢ = 1/f − 1/dₒ
  2. 1/dᵢ = 1/10 cm − 1/30 cm = 1/15 cm

dᵢ = 15 cm

Using the same 10 cm focal-length lens, if the object is moved to 20 cm away, how far from the lens does the image form?

  • 10 cm
  • 20 cm
  • 30 cm

For the original example (dₒ = 30 cm, dᵢ = 15 cm), what is the magnification, and what does it tell you about the image?

  • m = −0.5 — inverted and half size
  • m = 0.5 — upright and half size
  • m = −2 — inverted and double size