Concave Mirrors and Ray Diagrams

A concave mirror curves inward like the inside of a bowl, and it has a focal point F sitting halfway between the mirror and its center of curvature. To find an image, you trace three rays from the top of the object. The ray parallel to the axis reflects through F. The ray through F reflects back parallel to the axis. The ray through the center of curvature C hits the mirror straight on and reflects straight back on itself. Wherever two of these reflected rays cross, that is the top of the image. Draw any two and you are done.

Where the object sits controls everything about the image. Far outside the focal point, the image is real, inverted, and smaller, forming between F and C. Move the object in toward C, and the image shrinks toward the same size at C. Keep sliding it toward F, and the image grows larger and moves farther out, becoming inverted and larger beyond C. At exactly F, the reflected rays leave parallel and never meet, so the image vanishes to infinity. Push the object inside F, and the rays now diverge after reflecting; extending them backward gives a virtual, upright, magnified image behind the mirror, the shaving-mirror case.

This ray-tracing picture connects directly to the mirror equation, 1/do + 1/di = 1/f, which gives the same answers numerically instead of graphically, and to magnification m = -di/do, which tells you the size and orientation without drawing anything. Convex mirrors and lenses reuse this same logic, just with different sign conventions.