What you are looking at
An
object (the upright arrow) sits to the left of a thin lens. To find its image we
trace three
principal rays whose paths through the lens we already know. Where the
outgoing rays cross is the image. If the real rays cross on the far side, the image is
real and inverted (it can be projected on a screen); if only the backward extensions
cross (shown dashed), the image is
virtual, upright and on the same side as the object.
The three principal rays
Parallel ray (gold): enters parallel to the axis and is bent to pass through the far
focal point F.
Central ray (green): passes straight through the centre of the lens
undeviated.
Focal ray (blue): passes through the near focal point F first, then leaves
parallel to the axis. For a diverging lens the bent rays spread apart, so we follow their backward
extensions to the near focus instead.
The thin-lens equation
1/f = 1/dₒ + 1/dᵢ m = −dᵢ/dₒ
A
converging (convex) lens has f > 0; a
diverging (concave) lens has
f < 0. A positive dᵢ is a real image on the opposite side of the lens; a negative dᵢ is a virtual
image on the object's side. The magnification m gives size and orientation — negative is inverted,
|m| > 1 is enlarged.
Things to try
With a
converging lens, move the object inward: beyond 2f the image is real, inverted
and reduced (a camera); between 2f and f it is real, inverted and enlarged (a projector); and inside the
focal point f the image becomes
virtual, upright and magnified — that is a magnifying
glass. A
diverging lens always produces a virtual, upright, reduced image, which is why
such lenses are used to correct short-sightedness. You can also drag the object along the axis directly
on the diagram.