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Lesson 2 of 10Light & Geometric Optics
Unit 4 · Lesson 2 of 10

Rays, the Laws of Reflection and Plane Mirrors

Drawing light as rays, measuring angles from the normal, the two laws of reflection, specular versus diffuse reflection, and why a plane mirror image is the same size, upright, as far behind the mirror as you are in front, and virtual.

4 min read8 practice questionsAsk AI about this →

Key things to remember

  1. 1All angles are measured from the normal, the line perpendicular to the surface.
  2. 2Law of reflection: , and the incident ray, reflected ray and normal lie in one plane.
  3. 3Specular reflection (smooth surface) forms images; diffuse reflection (rough surface) scatters light but still obeys the law at each point.
  4. 4SALT describes an image: Size, Attitude, Location, Type.
  5. 5Plane mirror image: same size, upright, same distance behind the mirror, virtual, and laterally inverted.
  6. 6Real images form where light rays actually meet and can be projected; virtual images form where rays only appear to come from.

Look in a bathroom mirror and you seem to see a second room behind the glass, with a second you standing in it. There is no room back there, of course. Your brain assumes light travels in straight lines, so it traces the reflected rays backward and 'sees' the place they appear to come from. Understanding that one trick explains every image in this unit, and it starts with the simplest rule in optics: the law of reflection.

The language of rays

  • Incident ray: the ray of light arriving at a surface.
  • Reflected ray: the ray leaving the surface after bouncing.
  • Point of incidence: where the incident ray hits the surface.
  • Normal: an imaginary line drawn perpendicular (at ) to the surface at the point of incidence. Draw it dashed.
  • Angle of incidence : the angle between the incident ray and the normal.
  • Angle of reflection : the angle between the reflected ray and the normal.
Angles are measured from the normal, not the surface
This is the single most common error in the unit. If a ray makes with the mirror surface, the angle of incidence is . Every angle in reflection and refraction is measured from the normal.
plane mirrornormali = 40°r = 40°incident rayreflected rayLaw of reflection: ∠i = ∠r, measured from the normal.Incident ray, normal and reflected ray lie in one plane.Specular reflectionsmooth surface:rays stay parallelDiffuse reflectionrough surface:rays scatter
Fig 1An incident ray strikes a plane mirror and reflects; the dashed normal is perpendicular to the mirror and the angle of incidence equals the angle of reflection, both measured from the normal. Inset: specular reflection from a smooth surface versus diffuse reflection from a rough one.

The laws of reflection

  1. The angle of incidence equals the angle of reflection: .
  2. The incident ray, the reflected ray and the normal all lie in the same plane (you can draw all three on one flat sheet of paper).
ASpecular (regular) reflection
  • Smooth, polished surface: mirror, still water, glass
  • Parallel incident rays leave parallel
  • Forms a clear image
BDiffuse reflection
  • Rough surface: paper, wall, clothing
  • Parallel incident rays scatter in many directions
  • No image, but the object can be seen from anywhere in the room

Diffuse reflection still obeys the law of reflection at every single point. The surface is just bumpy on a tiny scale, so the normal points in a different direction at each point and the rays scatter. That is what lets you read this page from any angle, and why a wet road (smoothed by a film of water) suddenly reflects headlights like a mirror.

Images in a plane mirror

plane mirrorobjectvirtual imageeyeddSALT for a plane mirror imageS size: same as the objectA attitude: uprightL location: behind mirror, same distanceT type: virtual (laterally inverted)
Fig 2One ray from the tip of an object and one from its base reflect off a plane mirror into an eye. Extended backward as dashed lines, they lead to the tip and base of an upright, same-size virtual image, the same distance behind the mirror as the object is in front.

To locate an image, draw at least two rays from the same point on the object, reflect each one using , and extend the reflected rays backward (dashed) behind the mirror. Where the extensions meet is the image of that point. Because the reflected rays never actually pass through that point, the image is virtual: it cannot be caught on a screen. A real image is one where light rays actually meet, and it can be projected onto a screen.

SALT characteristicQuestion it answersPlane mirror image
SizeLarger, smaller or the same size as the object?Same size
AttitudeUpright or inverted (upside down)?Upright (but left and right appear reversed)
LocationWhere is the image?Behind the mirror, the same distance as the object is in front
TypeReal or virtual?Virtual
SALT is the checklist for describing any image formed by a mirror or lens.
Lateral inversion
Raise your right hand and your mirror twin raises the hand on the same side, which looks like its left. A plane mirror reverses front and back, which we perceive as left and right swapped. That is why AMBULANCE is printed backward on the front of an ambulance: in a driver's rear-view mirror it reads correctly.
How tall must a full-length mirror be?
Only half your height. Light from your feet hits the mirror halfway between your eyes and your feet on the way up to your eyes, and light from the top of your head hits it halfway between your eyes and your head. The answer does not depend on how far you stand from the mirror.

Worked examples

Reveal one step at a time and try to beat it to the next line.

Example 1
A ray of light strikes a plane mirror, making an angle of with the mirror surface. Find the angle of incidence, the angle of reflection, and the angle between the incident and reflected rays.
Example 2
Maya stands in front of a plane mirror. (a) How far is her image from her? (b) She walks toward the mirror. How far is she from her image now?
Example 3
A student who is tall wants a wall mirror in which she can see her whole body. What is the shortest mirror that works, and does it matter how far she stands from it?

Where marks get lost

  • Measuring the angle from the mirror surface instead of the normal. Always draw the normal first, then measure from it.
  • Saying the image is 'on the mirror' or 'in the glass'. A plane mirror image is behind the mirror, as far behind as the object is in front.
  • Calling a plane mirror image real because you can see it. You see virtual images too; a real image is one that can be projected onto a screen.
  • Thinking diffuse reflection breaks the law of reflection. Each point still obeys ; the rough surface just tilts the normal from point to point.
  • Believing you need a mirror as tall as you are, or that stepping back lets you see more of yourself. Half your height is enough, at any distance.

Flashcards 9

Normal
Law of reflection
Specular reflection
Diffuse reflection
+ 5 more

Practice

1
A ray strikes a plane mirror at to the mirror surface. What is the angle of reflection, in degrees?
°
2
The angle between an incident ray and its reflected ray is . What is the angle of incidence, in degrees?
°
3
Which statement describes the image in a plane mirror?
4
You stand in front of a plane mirror. How far are you from your image, in metres?
m
5
Why can you read a printed page from almost any angle, but see a clear reflection in a mirror only from certain positions?
6
In the SALT checklist for describing an image, what word does the T stand for?
7
What is the minimum height, in metres, of a plane mirror in which a tall person can see their full body? Give 2 decimal places.
m
8
Put the steps for locating the image of a point in a plane mirror in order.
  1. 1Mark the image where the dashed extensions cross
  2. 2Extend the reflected rays backward behind the mirror as dashed lines
  3. 3Draw each reflected ray so that the angle of reflection equals the angle of incidence
  4. 4Draw two rays from the object point to the mirror
  5. 5Draw the normal at each point of incidence

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