What you are looking at
An
object (the upright arrow) sits in front of a curved mirror. To locate its image we
trace a few
principal rays — special rays whose behaviour we already know. Where the
reflected rays cross is where the image forms. If the reflected rays themselves cross, the image is
real (you could catch it on a screen); if only their backward extensions cross
(drawn dashed), the image is
virtual, appearing behind the mirror.
The three principal rays
Parallel ray (gold): travels parallel to the axis, then reflects through the focal
point F.
Focal ray (blue): passes through F on the way in, then reflects parallel to
the axis.
Centre ray (green): heads toward the centre of curvature C and reflects
straight back on itself, because it strikes the mirror head-on. Any two of these are enough to fix the
image; the third is a check.
The mirror equation
1/f = 1/dₒ + 1/dᵢ m = −dᵢ/dₒ
Here f = R/2 is the focal length (half the radius of curvature). Using the convention that distances in
front of the mirror are positive: a
concave mirror has f > 0, a
convex
mirror has f < 0. A positive dᵢ means a real image in front of the mirror; a negative dᵢ means a
virtual image behind it. The magnification m tells you the size and orientation — negative m is inverted,
|m| > 1 is enlarged.
Things to try
With a
concave mirror, slide the object from far away inward: beyond C the image is real,
inverted and small; between C and F it is real, inverted and enlarged; and once inside the focal point F
the image jumps to
virtual, upright and magnified — this is the shaving/make-up mirror.
A
convex mirror always gives a virtual, upright, reduced image with a wide field of view,
which is why it is used for car wing-mirrors and shop security mirrors. You can also drag the object
left and right directly on the diagram.