Mirror Equation Calculator

Curved mirrors follow the same equation as thin lenses.

How the Math Works

The Mirror Equation Calculator uses the fundamental formula 1/f = 1/dₒ + 1/dᵢ, where f is the focal length of the mirror, dₒ is the object distance, and dᵢ is the image distance. This relationship stems from the geometric optics of spherical mirrors, describing how light rays converge or diverge after reflecting off the mirror's surface. By rearranging the formula, you can solve for any one variable if the other two are known, making it essential for determining image properties in curved mirror systems.

Practical Applications

To apply this calculation practically, first measure or determine the focal length of the mirror and the distance of the object from the mirror (dₒ). Input these values into the calculator to compute the image distance (dᵢ), which tells you where the reflected image will form. This is critical in designing optical instruments like telescopes, headlights, or microscopes, where precise image positioning ensures optimal performance and clarity for the user.

Day-to-Day Use

Understanding image distance through this formula helps in everyday scenarios involving mirrors, such as adjusting makeup or shaving mirrors for clearer views, optimizing security mirrors in stores to eliminate blind spots, or even in smartphone camera systems to improve image quality. It also aids in troubleshooting issues with reflective surfaces, ensuring that light is directed appropriately for safety or aesthetic purposes in daily life.

Worked example

object 20, f 8 → image 13.3.

FAQ