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 lens to object), and di is the image distance (from lens to image). It assumes the lens is thin relative to the distances involved.

What does a negative image distance mean?

A negative di means the image forms on the same side as the object — it is a virtual image. Virtual images appear upright and cannot be projected on a screen. This occurs when the object is inside the focal length of a converging lens, or with any diverging lens.

What does a negative focal length mean?

A negative focal length indicates a diverging (concave) lens, which spreads light rays apart. Diverging lenses always produce virtual, upright, and diminished images regardless of object placement.

How is magnification calculated?

Linear magnification is m = -di/do. A positive m means an upright image; negative m means an inverted image. |m| > 1 is magnified; |m| < 1 is diminished; |m| = 1 means same size as the object.

What sign convention does this calculator use?

This calculator follows the standard Cartesian sign convention: distances measured in the direction of incident light are positive. Object distance do is positive when the object is on the incoming-light side. Image distance di is positive for a real image on the opposite side, negative for a virtual image.

Thin Lens Calculator

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

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

Lens Parameters

Solve for

Focal Length (f) cm

Positive = converging lens; negative = diverging lens.

Object Distance (d_o) cm

Distance from object to the lens center.

Image Distance (d_i) cm

Positive = real image; negative = virtual image.

Select what to solve for, enter the two known values, and click Calculate.

Summary

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

How it works

Select which quantity you want to find: focal length, object distance, or image distance.
Enter the two known values in centimeters.
Click Calculate to apply 1/f = 1/do + 1/di and get the unknown value.
Read the magnification (m = -di/do) and image type — real or virtual, upright or inverted.
Try different values to compare converging (positive f) and diverging (negative f) lenses.

Use cases

Solve optics homework problems involving converging or diverging lenses.
Find where an image forms given a known focal length and object placement.
Determine what focal length a lens needs to produce an image at a target distance.
Check whether an image is real or virtual for a given lens setup.
Understand magnification in cameras, telescopes, and microscopes.
Explore how object distance affects image size and orientation.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu