Lens & Mirror Equation Calculator

This calculator applies the thin lens and mirror equation to find where an image forms and how large it is, from the focal length and the object distance. The same elegant equation governs both lenses and curved mirrors: one over the focal length equals one over the object distance plus one over the image distance. From it, and the object distance you provide, the calculator finds the image distance, and then the magnification, which tells you how much bigger or smaller the image is and whether it is upright or inverted. These ideas are the foundation of optics, explaining how spectacles, cameras, microscopes, telescopes, magnifying glasses and mirrors all form images. This tool takes the arithmetic out of it. You enter the focal length, positive for a converging lens or concave mirror and negative for a diverging lens or convex mirror, and the distance of the object, and the calculator returns the image distance, the magnification, and a clear statement of whether the image is real or virtual and upright or inverted. The results update as you type, so you can explore how moving an object toward or away from the focal point dramatically changes the image, from large and inverted to small or magnified and upright. Use it for physics homework, for understanding cameras and optical instruments, or for any optics problem. The sign conventions matter: a positive image distance means a real image that could be projected on a screen, formed on the far side of a lens, while a negative image distance means a virtual image, like the enlarged view in a magnifying glass, that only appears to be there. A negative magnification means the image is inverted.

1/f = 1/object + 1/image. Positive focal length: converging lens / concave mirror. Positive image distance = real image. Negative magnification = inverted.