Lensmakers Equation Calculator

What Is the Lensmakers Equation?

The lensmakers equation relates the focal length of a thin lens to its refractive index and the radii of curvature of its two surfaces. Optics designers use it to estimate how strongly a lens converges or diverges light.

Lensmakers Equation

$$\frac{1}{f} = (n - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$$

$f$ is focal length, $n$ is refractive index, and $R_1$ and $R_2$ are surface radii. Sign conventions matter: a convex surface facing the incoming light typically has positive $R_1$, while a concave surface on the exit side often has negative $R_2$.

Thin Lens Approximation

This formula assumes the lens thickness is small compared with the radii and focal length. For thick lenses or high-precision systems, more detailed optical design software is needed.

Explore related tools: Focal Length Calculator and Lens Magnification Calculator.

Frequently Asked Questions

What sign convention is used for radii?

We use the standard optics convention: radius is positive when the center of curvature lies to the right of the surface (for light traveling left to right).

What refractive index should I use for glass?

Common crown glass is about 1.5 to 1.52. Flint glass can be 1.6 or higher. Use the value from your material datasheet.

Can this equation give a negative focal length?

Yes. A diverging lens has negative focal length. The computed sign depends on surface curvatures and refractive index.

Can I solve for refractive index?

Yes. Select "Refractive Index" in the solve-for dropdown and enter focal length plus both radii.

Does this work for mirrors?

No. Mirrors follow different equations. This tool is for refracting thin lenses only.

Report

Lensmakers Equation Calculator

What Is the Lensmakers Equation?

Lensmakers Equation

Thin Lens Approximation

Frequently Asked Questions

Related Tools

Recent Visits