Geometrical Optics: Lenses and Mirrors

Geometrical optics describes the behavior of light by treating it as straight rays, an approach that works well for explaining how lenses and mirrors form images. A lens is a piece of transparent material, usually glass, shaped so that it bends light passing through it by refraction. A converging, or convex, lens brings parallel rays together at a point called the focus, while a diverging, or concave, lens spreads them apart. The distance from the lens to its focus, the focal length, determines how strongly the lens bends light.

Images are formed where the refracted rays meet, or appear to meet. A converging lens can produce a real image, which can be projected onto a screen, when the object is far enough away, or a magnified virtual image, as in a magnifying glass, when the object is close. The size, position, and orientation of the image depend on the focal length and on the distance between the object and the lens, a relationship that ray diagrams make clear. A “thick” lens model accounts for the actual thickness of real lenses rather than treating them as infinitely thin.

Mirrors form images by reflection rather than refraction, but the geometry is closely related. A curved mirror also has a focus and can produce real or virtual images depending on the object's position. Because these effects depend on angles and distances, interactive simulations are a natural fit: by dragging an object or changing a lens, a user can watch the rays redraw and the image shift, building an understanding of how optical instruments such as cameras, telescopes, and the eye work.

Frequently asked questions

What is the difference between a converging and a diverging lens?

A converging (convex) lens brings parallel rays together at a focus, while a diverging (concave) lens spreads them apart so they appear to come from a focus behind it.

What does focal length tell you about a lens?

It is the distance from the lens to its focus and indicates how strongly the lens bends light; a shorter focal length bends light more.

What is the difference between a real and a virtual image?

A real image forms where rays actually meet and can be projected onto a screen, while a virtual image only appears to come from where the rays seem to originate and cannot be projected.