# Thin Lens Equation Calculator

Created by Luciano Mino
Last updated: Aug 06, 2022

Our thins lens equation calculator can obtain the image distance of any object after being refracted by a lens of known focal length.

Within a few paragraphs, you will learn:

• What the thin lens equation is;
• How to calculate image distance using the image distance equation; and
• The magnification equation for lenses.

## Thin lens equation

The thin lens equation describes how the image of an object after crossing a thin lens is created.

This approximation considers that the width of the lens is much smaller than the object's distance.

To use it, we only need the focal length and the object's distance:

$\frac{1}{x}+\frac{1}{y} = \frac{1}{f}$

where:

• $x$ is the distance between the object and the center of the lens;
• $y$ is the distance between the image and the center of the lens; and
• $f$ is the focal length of the lens expressed in length units.

Thin lenses are especially important in telescopes when you want to observe various phenomena. Check the luminosity calculator and redshift calculator to learn more about astrophysics.

## How to calculate image distance

Let's see how to calculate image distance now.

We can rearrange the thin lens equation to obtain the image distance equation:

$y = \frac{fx}{x-f}$

where again:

• $x$ is the distance between the object and the center of the lens;
• $y$ is the distance between the image and the center of the lens; and
• $f$ is the focal length of the lens.

But generally speaking, it is easier just to plug the numbers in the thin lens equation and solve for distance.

💡 Even easier, type any two parameters in the thin lens equation calculator, and our tool will automatically complete the missing parameter!

## Magnification equation for lenses

Using the advanced mode of this thin lens equation calculator, we can find the magnification of a lens.

What is it? Magnification is the ratio between the height of the image and the height of the object, and it's equal to the ratio between image distance and object distance:

$M = \frac{|y|}{x}$

If you want to consider light going through different media, then you might need to use the index of refraction formula. We covered it in another article.

Luciano Mino
Object distance
in
Image distance
in
Focal length
in
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