Concave vs convex mirror images
How image type, size and orientation change with object position for concave and convex mirrors, and how the signs map to the math.
Why the sign convention matters
Curved mirror problems only make sense once you commit to a sign convention, and this calculator uses the common real-is-positive rule. A concave mirror curves inward like the inside of a spoon and converges light, so its focal length and radius are positive. A convex mirror bulges outward and spreads light, so its focal length and radius are negative. Keeping those signs straight is what lets a single equation, 1/f = 1/do + 1/di, describe both mirror types at once.
How a concave mirror behaves
A concave mirror is the interesting case because the image changes dramatically with distance. When the object sits beyond the center of curvature the image is real, inverted and smaller. Between the center and the focal point it becomes real, inverted and larger, which is why a shaving or makeup mirror magnifies when you lean in close. Move the object inside the focal length and the image flips to virtual, upright and enlarged. Right at the focal point the reflected rays are parallel and no image forms, which the calculator reports as an image at infinity.
How a convex mirror behaves
A convex mirror is far more predictable. For any real object in front of it the image is always virtual, upright and smaller than the object, and it appears to sit behind the mirror surface. That shrunken image packs a wide scene into a small area, which is exactly why convex mirrors are used for car passenger-side mirrors and store security domes. Because the image is virtual, the image distance always comes out negative, and the magnification is always a positive fraction less than one.
Reading the calculator output
The result cards translate the algebra into plain physics. A positive image distance means a real, inverted image and a negative one means a virtual, upright image, which is the label shown beneath the numbers. The magnification sign echoes that orientation and its size tells you how much bigger or smaller the image is. Cross-check any answer by confirming the focal length is positive for a concave setup and negative for a convex one, since a flipped sign is the most common mistake in mirror problems.