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Physics

Thin Lens Equation

1/f = 1/do + 1/di. Free online Thin Lens Equation. Calculate thin lens equation online — fast, accurate, mobile-friendly, no signup needed.

1/f = 1/u + 1/v.
Image dist (cm)
40

Derivation

  1. ├── 01Givenf = 20, do_ = 40
  2. ├── 02Formulat × a / (a-t)
  3. └── 03Compute Image dist (cm)40
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§01What is

Understanding the Thin Lens Equation

The Thin Lens Equation computes Image dist (cm) from 2 inputs: focal length (cm), object dist (cm). 1/f = 1/do + 1/di.

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Thin Lens Equation sits in that toolkit — it 1/f = 1/do + 1/di. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

t × a / (a-t)

Where

f
Focal length (cm)
do_
Object dist (cm)
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Focal length (cm) = 20, Object dist (cm) = 40.

  1. 01Start by noting the input — Focal length (cm): 20.
  2. 02Start by noting the input — Object dist (cm): 40.
  3. 03Substitute these values into the formula: t × a / (a-t)
  4. 04Compute Image dist (cm): the calculator returns 40.
  5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Thin Lens Equation Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Focal length (cm) halved

f = 10 (from 20)

Keep every other input at its default and halve the focal length (cm). See how image dist (cm) responds.

  1. 01New Focal length (cm): 10
  2. 02Baseline Image dist (cm): 40
  3. 03New Image dist (cm): 13.3333
  4. 04Image dist (cm) decreases by 66.7% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Object dist (cm) doubled

do_ = 80 (from 40)

Keep every other input at its default and double the object dist (cm). See how image dist (cm) responds.

  1. 01New Object dist (cm): 80
  2. 02Baseline Image dist (cm): 40
  3. 03New Image dist (cm): 26.6667
  4. 04Image dist (cm) decreases by 33.3% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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