Mirrors & Lenses

A real image forms where light rays actually converge, so it can be projected onto a screen and the simulator marks it with a solid green arrow. A virtual image forms where rays only appear to come from, behind the lens or mirror; it cannot be projected and is drawn as a dashed yellow arrow. In the maths a positive image distance d_i means real, while a negative value means virtual.

It uses the thin-lens and mirror equation 1/f = 1/d_o + 1/d_i, rearranged to 1/d_i = 1/f - 1/d_o. Converging elements take a positive focal length and diverging ones a negative focal length. The magnification is then m = -d_i/d_o, and image height is m times the object height.

They are the standard principal rays used to construct an image. The red ray travels parallel to the optical axis and then passes through the focal point F'. The green ray goes straight through the centre of the lens (or to the centre of a mirror) undeviated. The blue ray passes through the near focal point F and emerges parallel to the axis. Dashed segments are virtual extensions used to locate virtual images.

A diverging lens has a negative focal length, so 1/d_i = 1/f - 1/d_o is always negative for a real object. That makes the image distance negative, meaning the image is always virtual, upright and reduced in size. A convex mirror behaves the same way, which is why it is used for wide-angle car and shop mirrors.

It uses the ideal thin-lens approximation, which assumes the lens is infinitely thin and rays stay close to the axis (the paraxial regime). That makes it a faithful teaching model, but it ignores real-world effects such as spherical and chromatic aberration, lens thickness and finite aperture. Distances are shown in pixels rather than physical units, so it illustrates the relationships rather than predicting a specific camera or telescope.