Equação do Espelho Esférico
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
1/f = 1/d_o + 1/d_i
About this calculator
The Spherical Mirror Equation calculator solves the relationship between focal length (f), object distance (d_o), and image distance (d_i) for spherical mirrors (concave or convex). The formula used is 1/f = 1/d_o + 1/d_i, known as the Gaussian mirror equation. You can calculate any of the three variables by providing the other two. The result includes the nature of the image (real or virtual, inverted or upright) and magnification.
How it works: the equation relates distances in meters (or any consistent unit). For concave mirrors, f is positive; for convex mirrors, f is negative. d_o is always positive if the object is in front of the mirror. d_i is positive for real images (formed in front of the mirror) and negative for virtual images (behind the mirror). Magnification (m = -d_i/d_o) indicates whether the image is larger or smaller than the object and whether it is inverted (m negative) or upright (m positive).
When to use: ideal for high school or college physics students solving spherical mirror problems. Useful for professionals designing simple optical systems such as reflecting telescopes or makeup mirrors. The calculator helps quickly verify whether the image formed is real or virtual, inverted or upright, and its relative position.
Cautions: ensure correct signs for f and d_i according to sign conventions (f positive for concave, negative for convex; d_i positive for real image, negative for virtual). The equation assumes spherical mirrors with small aperture (paraxial rays). For objects very close to the mirror, spherical aberrations may occur that the formula does not account for. Always check unit consistency.
Frequently asked questions
What does a negative focal length mean?
A negative focal length indicates a convex mirror. Convex mirrors always produce virtual, smaller, and upright images.
How do I know if the image is real or virtual?
If the image distance (d_i) is positive, the image is real and formed in front of the mirror. If negative, it is virtual and formed behind the mirror.
Does the calculator work for plane mirrors?
Not directly. Plane mirrors have infinite radius of curvature, so f is infinite. The equation becomes 1/d_o + 1/d_i = 0, giving d_i = -d_o, a virtual image of the same size.
Can I use any unit of distance?
Yes, as long as all distances are in the same unit (meters, centimeters, etc.). The result will be consistent.
What is magnification and how to interpret it?
Magnification (m) is the ratio of image size to object size. If m is negative, the image is inverted; if positive, upright. |m| > 1 means larger image; |m| < 1 means smaller image.