Reflection of light and images in a plane mirror
Light reflects with ∠i = ∠r. A plane mirror forms a virtual, erect, same-size image, as far behind the mirror as the object is in front.
Reflection and its two laws
- Objects that give out their own light, such as the Sun, a burning candle or a glowing bulb, are luminous. The Moon and a steel plate only send back light that falls on them, so they are non-luminous.
- Reflection is the bouncing back of light from a surface. A smooth, shiny surface that reflects most of the light is a mirror.
- The ray that falls on the surface is the incident ray. The ray that bounces back is the reflected ray.
- The normal is a line drawn at 90° to the surface at the point where the ray falls. Both angles are measured from the normal, not from the mirror.
- Law 1: the incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane.
- Law 2: the angle of incidence equals the angle of reflection: ∠i = ∠r.
- In reflection the speed, frequency and wavelength of light do not change.
- Our eyes see light of wavelength about 400 nm (violet) to 700 nm (red). Longer waves are infrared and shorter ones are ultraviolet.
Regular reflection vs diffused reflection
Each tiny part of a rough surface still obeys the laws of reflection. Only the normals point in different directions.
The image in a plane mirror
| Property | What it means |
|---|---|
| Virtual | The reflected rays only seem to come from behind the mirror. The image cannot be caught on a screen. A real image is where rays actually meet, so it can be caught on a screen. |
| Erect | The image is upright, the right way up. |
| Same size | The image is exactly as big as the object. |
| Same distance | The image is as far behind the mirror as the object is in front, on the same normal: OA = OA′. |
| Lateral inversion | Left and right are swapped. Your left hand looks like the image's right hand. |
| Moving object | If you walk towards the mirror at speed v, your image also moves towards the mirror at v. It comes towards you at 2v. |
| Full-length image | A mirror only half your height is enough to see yourself from head to toe. |
| Two mirrors at an angle θ | Number of images n = (360°/θ) − 1 when 360°/θ is even. At 90° you get 3 images; at 60° you get 5. |
Activity (practical): verify the laws of reflection with a plane mirror strip
You need a mirror strip in a stand, a drawing board, white paper, four pins, a scale and a protractor.
- 1Pin a white sheet on a drawing board. Draw a straight line M₁M₂ near the middle.
- 2Stand a thin plane mirror strip upright in a wooden stand, with its reflecting surface along M₁M₂.
- 3Draw a slanting line towards the mirror. Fix two pins, A₁ and A₂, upright on it, at least 6 cm apart.
- 4Look into the mirror from the other side. Fix two more pins, B₁ and B₂, so that they and the images of A₁ and A₂ all appear in one straight line.
- 5Remove the mirror and pins. Join B₁B₂ and extend it to M₁M₂. Extend A₁A₂ to meet it at O, the point of incidence.
- 6Draw the normal ON at 90° to M₁M₂ at O. Measure ∠i (between A₂O and ON) and ∠r (between OB₁ and ON) with a protractor.
- 7Repeat for three different angles of incidence and record them in a table.Observe: ∠i = ∠r every time, within small errors. The rays and the normal are all on the flat paper, so they lie in one plane.
How to draw the image of a point object in a plane mirror
- 1Draw a straight line for the mirror and shade short slanting lines behind it.
- 2Mark a point object A in front of the mirror.
- 3Draw two rays from A to the mirror at two different points. Draw a dotted normal at each point.
- 4Draw each reflected ray so that it makes the same angle with the normal as its incident ray. Add arrowheads.
- 5Extend both reflected rays backwards as dotted lines behind the mirror. They meet at A′, the virtual image.
- 6Join A and A′ with a dotted line. Show that it is at 90° to the mirror, and mark the two equal distances.
Plane mirror: distances and speeds
A girl stands 1.5 m in front of a plane mirror on a cupboard door. (a) How far is her image from her? (b) She walks 0.5 m towards the mirror. How far is the image from her now? (c) She walks towards the mirror at 1 m/s. How fast does her image come towards her?
- (a) The image is as far behind the mirror as she is in front: 1.5 m behind.
- Distance from girl to image = 1.5 m + 1.5 m = 3.0 m.
- (b) New distance from the mirror = 1.5 m − 0.5 m = 1.0 m, so the image is 1.0 m behind it.
- Distance from girl to image = 1.0 m + 1.0 m = 2.0 m.
- (c) The image moves towards the mirror at 1 m/s, while she moves towards it at 1 m/s.
- So the image comes towards her at 1 m/s + 1 m/s = 2 m/s.
(a) 3.0 m; (b) 2.0 m; (c) 2 m/s
The word AMBULANCE is painted back to front on the bonnet, so a driver ahead reads it the right way in the rear-view mirror. A dressing mirror only half your height shows you from head to toe.
1 marks: “A ray of light strikes a plane mirror at 90° to its surface. What are the angle of incidence and the angle of reflection?” Both are 0°. The ray falls along the normal and goes back along the same path.
2 marks: “Distinguish between regular and diffused reflection, with one example of each.” Regular: at a smooth surface, parallel rays stay parallel and form an image (a mirror, still water). Diffused: at a rough surface, rays scatter in all directions and form no image (paper, a wall). Both obey the laws of reflection.
3 marks: “State the two laws of reflection. A ray makes an angle of 25° with the surface of a plane mirror. Find the angle of reflection and the angle between the incident and reflected rays.” Law 1: incident ray, reflected ray and normal lie in one plane. Law 2: ∠i = ∠r. Here ∠i = 90° − 25° = 65°, so ∠r = 65°. Angle between the rays = 65° + 65° = 130°.
In equals out, all on one page: angle in = angle out, and both rays and the normal lie in one plane.