Thin Lens Equation

Also known as lens formula · 1/f = 1/do + 1/di · lensmaker's relation

1f=1do+1di\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}

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Learning zone

The thin lens equation is the workhorse of geometric optics, tying together where the object sits, where its image forms, and the lens's focal length. The sign conventions carry the physics: a positive d_i is a real image on the far side of a converging lens, a negative d_i a virtual image on the near side. Place an object exactly at the focal point and 1/d_i must vanish — the image recedes to infinity, which is how a magnifying glass produces parallel rays.

A camera focused on a subject 2 m away with a 50 mm lens forms its image at d_i = (1/0.05 − 1/2)⁻¹ ≈ 51.3 mm behind the glass — the millimeter of travel that the focus ring provides.

Thin Lens Equation
1f=1do+1di\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}
Where
  • ff= Focal length
  • dod_o= Object distance
  • did_i= Image distance
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