# Thin Lens Equation Calculator

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.

Keep reading to learn **more** about optical lenses with this lens calculator 🔎!

## 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:

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:

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**:

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.