Laws of reflection

The angle of incidence equals the angle of reflection, both measured from the normal
The incident ray, the reflected ray and the normal lie in the same plane

Reflection is the same for every wavelength, so mirrors have no chromatic aberration

## Plane mirrors

The image is virtual, erect, the same size, and as far behind the mirror as the object is in front
It is laterally inverted (left and right swapped)
Rotating a mirror through an angle θ rotates the reflected ray through 2θ

A plane mirror doubles the test distance in a short room: a reversed chart viewed in a mirror 3 m away is seen at 6 m. The letters are printed reversed so they read correctly.

## Spherical mirrors: terms

Centre of curvature (C): the centre of the sphere of which the mirror is part. Radius r
Principal focus (F): where light parallel to the axis meets (concave) or appears to diverge from (convex)

F lies halfway between the mirror and C: f = r/2
Concave mirrors converge light (a plus power). Convex mirrors diverge it (a minus power)

Mirror formula, taking distances to real objects and real images as positive: 1/u + 1/v = 1/f = 2/r

A negative v means a virtual image behind the mirror. For a convex mirror f is negative
Magnification = image size ÷ object size = v/u

To locate an image, draw two of these rays from the top of the object

A ray parallel to the axis reflects through F (concave), or as if from F (convex)
A ray through C (or aimed at C) reflects straight back on itself
A ray through F reflects parallel to the axis

## Concave mirrors

Object position	Image
Beyond C	Between C and F: real, inverted, diminished
At C	At C: real, inverted, same size
Between C and F	Beyond C: real, inverted, magnified
At F	At infinity (reflected light is parallel)
Inside F	Behind the mirror: virtual, erect, magnified (shaving or make-up mirror)

Worked example: an object 30 cm from a concave mirror with r = 20 cm (f = 10 cm)

1/v = 1/10 − 1/30 = 2/30, so v = +15 cm: a real image 15 cm in front of the mirror
Magnification = 15/30 = 0.5: inverted and half size

## Convex mirrors

The image is always virtual, erect and diminished, between the mirror and F, wherever the object is
It gives a wide field of view: car wing mirrors and shop security mirrors
Worked example: an object 20 cm from a convex mirror with f = −10 cm

1/v = −1/10 − 1/20 = −3/20, so v = −6.7 cm: virtual, 6.7 cm behind the mirror
Magnification = 6.7/20 = 0.33: erect and one third the size

The anterior cornea acts as a convex mirror. The keratometer measures the size of the reflected image of its mires

For a distant object, r ≈ 2d × I/O, where d is the object distance, I the image size and O the object size
Worked example: a 50 mm mire at 100 mm forms a 1.95 mm image, so r = 2 × 100 × 1.95 ÷ 50 = 7.8 mm (see keratometry)

## Catoptric (Purkinje–Sanson) images

Images I, II and III are formed by surfaces that act as convex mirrors: the anterior cornea, the posterior cornea and the anterior lens

Erect, virtual, diminished
Image I is the brightest, because the air–tear interface has the largest change in refractive index
Image III is the largest, because the anterior lens surface is the flattest (radius about 10 mm)

Image IV is formed by the posterior lens surface, which acts as a concave mirror

Real, inverted, and small

Uses of catoptric images:

Image I: keratometry and Placido-disc topography measure corneal curvature from it, and the Hirschberg and Krimsky tests use its position (the corneal light reflex) to detect strabismus
In accommodation, image III becomes smaller and moves forward because the anterior lens surface steepens; images I and IV barely change. This was the original evidence that accommodation changes the lens
The separation of images I and II depends on corneal thickness, and of II and III on anterior chamber depth
Dual-Purkinje eye trackers compare images I and IV, and their alignment shows IOL tilt and decentration

Mirrors in instruments: the retinoscope mirror (see retinoscopy), the mirrors of gonioscopy lenses (see Gonioscopy), and the mirror or prism that turns the light path in ophthalmoscopes and slit lamps.