What is the thin lens equation?

The thin lens equation is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance from the lens, and di is the image distance from the lens. All distances are measured in the same unit (centimeters here).

What does a negative focal length mean?

A negative focal length indicates a diverging (concave) lens. Diverging lenses always produce virtual, upright, and reduced images regardless of the object position.

What does a negative image distance mean?

A negative image distance means the image is virtual — it forms on the same side as the object. Virtual images cannot be projected onto a screen but can be seen by looking through the lens.

How is magnification calculated?

Linear magnification m = -di / do. If |m| > 1 the image is enlarged; if |m| < 1 it is reduced. A negative m means the image is inverted; positive m means upright.

Can object distance be negative?

In the standard sign convention, object distance is positive when the object is on the incoming-light side of the lens (the normal case). Negative do occurs in compound lens systems where a virtual object is used.

What happens when the object is at the focal point?

When do equals f, the lens equation produces 1/di = 0, meaning the image forms at infinity. In practice, parallel rays exit the lens and never converge to form an image.

Lens Equation Calculator

Name: Lens Equation Calculator
Availability: InStock
Author: Nham Vu

Enter any two of focal length, object distance, or image distance to solve the thin lens equation instantly.

Thin Lens Equation

1 / f = 1 / d_o + 1 / d_i

Solve for

Object Distance (d_o) — cm

Image Distance (d_i) — cm

Sign Convention

f > 0 Converging (convex) lens
f < 0 Diverging (concave) lens
d_i > 0 Real image (opposite side)
d_i < 0 Virtual image (same side)

Enter two values and click Calculate to solve the lens equation.

Summary

Enter any two of focal length, object distance, or image distance to solve the thin lens equation instantly.

How it works

Select which variable you want to solve for: focal length (f), object distance (do), or image distance (di).
Enter the two known values in centimeters.
Click Calculate — the tool applies the thin lens equation to find the unknown.
Review the result: image distance, magnification, and image properties are displayed.
Use negative values for diverging lenses (negative f) or virtual images (negative di).
Clear the form and try different inputs to explore how lenses behave.

Use cases

Physics students solving optics homework problems.
Lab technicians verifying focal lengths of unknown lenses.
Photographers calculating minimum focus distances.
Teachers demonstrating real vs. virtual image formation.
Engineers designing projection systems or microscopes.
Science enthusiasts exploring how converging and diverging lenses differ.

Frequently Asked Questions

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Last updated: 2026-05-23 · Reviewed by Nham Vu