By carefully drawing ray diagrams to scale, we can determine the exact characteristics of an image formed by a thin lens or spherical mirror. The image and its characteristics may also be found using equations.

In drawing ray diagrams, we follow certain conventions:

Object distances are positive for real objects.

Image distances are positive for real images, negative for virtual images. Another way to think of this is: images that end up "downstream" have positive image distances; images that end up "upstream" have negative image distances.

Focal lengths are positive for convex lenses, negative for concave lenses.

Magnification is positive for an upright image, negative for an inverted image. The absolute value of the magnification (in other words, ignoring the negative which means inverted) is <1 for a smaller image, =1 for a same-size image, and >1 for a larger image.

A thin lens may be approximated by a line, a spherical mirror should be drawn to scale.

For drawing ray diagrams of lenses and mirrors (either concave or convex), three rays are useful:

A ray which leaves the object parallel to the axis lines up with a focus after interacting with the lens or mirror.

A ray which leaves the object in line with a focus is parallel after interacting with the lens or mirror.

A ray which passes through the center of a lens will be unrefracted.

A ray which goes along the central axis of a mirror will reflect back along itself.

A ray which travels at an angle to and strikes the central axis of a mirror will follow the law of reflection (as all rays striking a mirror do) and reflect off at the same angle it came in on.

A real image can be projected onto a screen, a virtual image cannot.

A real image is the result of light rays which converge.

A virtual image is the result of your brain's interpretation of diverging rays. Your brain always thinks the rays came from a place where they converged.

Convex lenses produce real inverted images for an object beyond f. If the object is:

Beyond 2f, the image is beyond f and smaller.

At 2f, the image is also at 2f and the same size as the object.

Between 2f and f, the image is enlarged.

For an object inside f, a convex lens produces an upright, enlarged, virtual image.

Concave lenses always produce upright, virtual, reduced images no matter where you place the object.

Concave mirrors form real, inverted, enlarged images for objects beyond f.

Concave mirrors form virtual, upright, enlarged images for objects inside f.

Convex mirrors always form virtual, upright, reduced images, no matter where you put the object.