# Lens Maker Equation Calculator

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Adena Benn
Last updated: Jun 05, 2023

Our lens maker equation calculator is a tool that helps to choose the appropriate parameters to obtain a specific focal length of the lens. You can change the material's geometric settings and the refractive index. Continue reading to learn about lens design and applications and how you can use our lens calculator to determine the focal length. If you want to hear more about the light refraction mechanism, check out our Snell's law calculator.

## Why do we need lenses?

• Human eye is a natural lens where the muscles control the focal length (they can change the shape of the lens). However, some people have eyes whose lenses do not focus light correctly, and therefore they need to use glasses - artificial lenses.

• With the appropriate arrangement of lenses, we can construct microscopes that can magnify tiny objects and telescopes which can magnify objects that are far away. Check our thin lens calculator if you want to learn about the magnification of a simple lens and our telescope magnification calculator if you wish to learn more about how a telescope works.

• Another application of lenses is a camera. Just like the eye muscles, a system of lenses can change its focal length (by sliding lenses along the camera) to focus the image on the camera film.

## Focal length calculator

You can estimate the focal length of the lens in the air using the mathematical formula below:

1/f = (n - 1) * (1/R1 - 1/R2 + (n - 1) * d / (n * R1 * R2)

where

• f is the focal length;
• n is the refractive index of the lens material;
• R1 is the radius of curvature of the lens surface closest to the light source;
• R2 is the radius of curvature of the lens surface farthest from the light source; and
• d is the thickness of the lens.

The above equation reduces to the simpler version if we assume that the lens is very thin (d = 0):

1/f = (n - 1) * (1/R1 - 1/R2)

In most cases, lenses are thin enough to justify the use of the simplified formula. If you want to change the thickness of the lens, too, switch to the advanced mode of our calculator. We encourage you to check the numerical difference between both equations.

The radius of curvature can be both a positive and a negative number. Briefly, a spherical lens usually consists of two surfaces: left and right, which can both be convex or concave. In our calculator, we have used Cartesian sign convention:

• Convex lens: left surface R1 > 0, right surface R2 < 0,
• Concave lens: left surface R1 < 0, right surface R2 > 0.
Dominik Czernia, PhD
in
in
Refractive index
Focal length
in
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