Thin Lens Equation Calculator

1/f = 1/d_o + 1/d_i. Solve for any of focal length, object distance, image distance.

Inputs

Result

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General calculation reads

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Scientific calculator (Casio fx-991EX)
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How to use this calculator

  • Pick which to solve.
  • Enter the other two.
  • Read result + magnification.

About this calculator

Thin lens equation: 1/f = 1/d_o + 1/d_i. Sign conventions: f positive for converging (convex) lens, negative for diverging (concave). d_o positive for real object (in front). d_i positive for real image (other side); negative for virtual (same side). Magnification M = -d_i/d_o; |M| > 1 enlarged, |M| < 1 reduced. Negative M = inverted (real image), positive = upright (virtual). Used in cameras, telescopes, microscopes.

Frequently asked

Sign convention?+
Cartesian. f >0 converging. d_o >0 real object. d_i >0 real image. d_i <0 virtual (same side as object).
Magnification > 1?+
Image is bigger than object. Microscope/eyepiece. M < 1: smaller (camera taking landscape).
When is image virtual?+
Object inside focal length of converging lens, or any object with diverging lens. Magnifying glass: object < f โ†’ virtual upright magnified.
Camera lens?+
For distant objects: d_i โ‰ˆ f. Sensor distance from lens equals focal length. 50mm lens means f = 50mm.
Thin vs. thick lens?+
Thin lens: ignores lens thickness. Real lenses use principal planes. Good approximation for f >> thickness.

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