Reflection of light and mirrors

A mirror makes space appear behind its surface, yet the reflected light does not travel there. How does the same reflection rule for each ray produce a whole image?

To compare light falling on different surfaces, we need a common reference line. At the point where the ray meets the mirror, draw the normal: a line perpendicular to the surface. The angle of incidence α is measured between the incident ray and this normal, in degrees. If the ray follows the normal, α = 0°, while its angle to the surface is 90°. This simple check prevents confusing the two angles.

Experiments with a smooth mirror give the law: the reflection angle β equals the incidence angle α, so β = α. Both are measured from the normal; the incident ray, reflected ray and normal lie in one plane. Draw the outgoing ray symmetrically to the incident ray about the normal. Increasing α by 10° also increases β by 10°; at α = 0° light returns along the same line. Arrows distinguish travel towards and away from the mirror.

Why does a mirror reflect light in an ordered way while paper sends it in many directions? Neighbouring regions of a smooth plane mirror have parallel normals, so incident rays with the same direction also reflect in the same direction. Small regions of a rough surface tilt differently: their normals and reflected directions differ. Each region still obeys β = α. Diffuse reflection does not mean that the law is randomly broken.

White paper can be seen from many places because its reflected light spreads in different directions. A mirror can also send light into the eye, but the directions remain linked to each object point in a way that forms a sharp image. Imagine roughening the mirror: light does not disappear, but this ordered relation between directions is disrupted and the image blurs. Preserving that relation distinguishes image-forming reflection from simply illuminating a surface.

Take an object point and two rays that enter the eye after reflection. Their directions make the light appear to have travelled straight from a point behind the mirror. Extend the reflected rays backwards: their extensions meet there. This is the original point's virtual image. Light really enters the eye and the image is visible, but those rays do not actually meet behind the mirror.

Equal angles imply symmetry: each image point lies behind a plane mirror at the same perpendicular distance as the object point in front. The image is therefore upright and the same size. Move the object one metre farther away and the image moves one metre farther behind the mirror; their separation grows by two metres. Do not confuse the image's size with how large it looks from a chosen viewpoint.

Putting a screen where the image appears to be is not enough: the real reflected rays do not arrive there. The virtual image therefore cannot be projected onto a screen at that position. Draw actual paths as solid arrowed lines and backward extensions as dashed lines. This distinction checks the construction's physical meaning: an image seen by the eye need not be formed by light gathering at its apparent location.

An incident ray makes an angle of 30° with a mirror surface. Find the angles of incidence and reflection.

The given 30° is measured from the surface. The normal is perpendicular to it, so the angle of incidence is α = 90° − 30° = 60°.

By the reflection law, β = α = 60°. Measure this second angle from the normal too, keeping the same reference line.

Symmetry check: the reflected ray also makes 30° with the surface. Thus the answer 60° agrees with both the given angle and the law.

Incidence angle: 60°; reflection angle: 60°. Both are measured from the normal to the mirror.

The law β = α concerns angles from the normal and also applies to individual regions of a rough surface.

A plane mirror preserves the relation between ray directions and gives an image symmetric to the object about its plane.

Arriving rays make a virtual image visible, but only their extensions meet at its position, so a screen there cannot receive it.

Light can change direction on entering another transparent medium. This enables lenses to form images.