Thin Lens Calculator

1/f = 1/dₒ + 1/dᵢ

Thin lens equation calculator — find image distance from focal length and object distance. 1/f = 1/dₒ + 1/dᵢ.

Calculate

Focal length f (m)

Object distance dₒ (m)

Enter values above to calculate

How it calculates

1/dᵢ = 1/f − 1/dₒ

dᵢ = 1 / (1/f − 1/dₒ)

Positive dᵢ = real image; negative = virtual image

Formula

1/f = 1/dₒ + 1/dᵢ

Variable Table

Symbol	Quantity	SI Unit
f	Focal length	m
dₒ	Object distance	m
dᵢ	Image distance	m
M	Magnification = −dᵢ/dₒ	—

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How to Use This Calculator

This thin lens calculator is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.

Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.

Assumptions and Limits

The formula 1/f = 1/dₒ + 1/dᵢ is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.

Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.

Worked Example

Converging lens f = 0.1 m, object at dₒ = 0.3 m. Find image distance.

Step 1: 1/dᵢ = 1/0.1 − 1/0.3 = 10 − 3.333 = 6.667

Step 2: dᵢ = 1/6.667

Answer: dᵢ = 0.15 m (real image)

Common Mistakes

Sign convention: converging lens f > 0, diverging f < 0
Object at focal point (dₒ = f) produces image at infinity
Real images (dᵢ > 0) form on the opposite side; virtual (dᵢ < 0) on the same side

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Frequently Asked Questions

What is the sign convention?

In the "real-is-positive" convention: f > 0 for converging lenses, dᵢ > 0 for real images, dᵢ < 0 for virtual images.

What is magnification?

M = −dᵢ/dₒ. Negative M means inverted image; |M| > 1 means enlarged.