Reflection in plane mirrors

You will find details of plane reflection in the 11-14 section of the site but some basic facts will be summarised here with a few more advanced topics.

Plane mirror

The reflection of light from a plane mirror can be summarised by the following laws:
1. The angle of incidence (i) is equal to the angle of reflection (r)
2. The incident ray, reflected ray and the normal to the surface at the point of incidence all lie in the same plane.

The reflection from a plane (flat) mirror is shown in Figure 1. Not the normal line and the use of shading to represent the back of the mirror.

Remember that with a glass mirror the reflecting surface (usually a thin layer of aluminum or silver) is placed on the back of the mirror and then covered with a protective layer. This means that although the main reflected image comes form this surface light will also reflect from the front surface of the glass. This will give a secondary image which is much weaker that the main image. This is usually invisible in every day life but would create severe problems in astronomy. For this reason all astronomical mirrors have their reflecting surface formed on the front of the glass.

Images

There are two types of image

(a) a Real Image

This is one through which the light rays actually pass and which can be formed on a screen. Examples of real images are the image formed on the film in a camera or on the retina of your eye

(b) a Virtual Image

This is one through which the rays do not pass, they only appear to come from it. Examples of virtual images are the image formed by a magnifying glass when used to look at a small object and that in a plane mirror.

For a real object, the image produced by a plane mirror is virtual and the same distance (d) behind the mirror as the object is in front of it. (see Figure 2).

Inclined mirrors

If the image of an object is viewed in two plane mirrors that are inclined to each other more than one image is formed. The number of images depends on the angle between the two mirrors.

The number of images formed in two plane mirrors inclined at an angle A to each other is given by the formula:
Number of images = 360/A - 1

Figure 3 shows the case for an angle of 60^o between the mirrors. As the angle gets smaller (down to 0^o when the mirrors are facing each other and parallel) the smaller the angle the greater the number of images.
Try seeing this in a room where there are mirrors on two facing walls.

Rotating mirrors

When a mirror rotates through an angle θ a beam of light reflected from it will rotate through an angle of 2θ.
(See Figure 4).

Lateral inversion

The image produced by a plane mirror is laterally inverted - that is reversed left to right. Look at yourself in a plane mirror and raise your fight hand - your image raises its left hand. In fact what is actually happening is that the image is reversed back to front.

Uses of plane mirrors

Looking into!Optical lever
Seeing round corners
Dental mirror
Periscope (See Figure 5)
Telescope flat
Illuminating Egyptian tombs
Kaleidoscope
Overhead projector
Sextant (See: OHT sheets/Sextant)

Reflection properties

When light falls on a surface three things may happen:-
(a) a fraction r will be reflected
(b) a fraction a will be absorbed and
(c) a fraction t will be transmitted
For any surface these fractions must add up to 1.
Therefore :- r + a + t = 1

Magnesium oxide will reflect some 98% of the incident light; silver is also a very good reflector over a fairly limited range of wavelengths but does tarnish with age and aluminum although not quite so reflective gives a better reflection over a wider range of wavelengths.
The absorption of light as it passes through a material is very important especially in the area of fibre optic communication systems (see later).

The intensity (I) of light transmitted through a material of thickness x is given by the equation:

I=I₀e^-mx

where µ is a constant for the material. For a specimen of glass µ could be 4 m^-1 at 600 nm wavelength yellow light) rising to 1000 m^-1 at a wavelength of 250 nm (ultra violet), the larger the value of m the more the light is absorbed. This means that if a beam of yellow light passed through 0.1 m of glass it would be reduced to 67% of its original intensity.

The absorption of differing wavelengths as they pass through the Earth's atmosphere is vital in communications and the transmission of ultra violet light through the "ozone hole"!

Mirrors used for reflecting telescopes are made with front-silvered mirrors to present unwanted multiple reflections from within the glass and also to reduce absorption within it.

One way mirrors are an interesting application of reflection. A thin metal film is deposited on a glass sheet so that only part of the incident light is transmitted. Standing on the poorly lit side of such a minor enables you to see through to the bright side but when viewed from the other side it looks like a perfect mirror.