Every time you check a mirror, read a road sign at night, or watch light bounce off a still lake, you are seeing one simple rule in action. The angle a wave arrives at equals the angle it leaves, measured from a line drawn perpendicular to the surface. Master this and the ray diagrams that follow, and you hold the key to mirrors, periscopes and the geometry of every reflected wave.
You shine a laser pointer at a flat mirror so that the beam hits at a steep angle, almost straight on.
Before reading: where does the reflected beam go, straight back along the same path, off at a wide angle, or somewhere in between? From which line should the angle be measured? Write your prediction and one sentence of reasoning.
The angle of incidence equals the angle of reflection, both measured from the normal
When a wave bounces off a surface, it leaves at exactly the same angle it arrived, and the line we measure both angles from is the normal, drawn at right angles to the surface.
The law of reflection has two parts:
Law of reflection: the angle of incidence equals the angle of reflection, $\theta_i = \theta_r$, with both angles measured from the normal (the line perpendicular to the surface). The incident ray, reflected ray and normal lie in one plane.
Pause, copy the highlighted statement into your book before moving on.
Did you get this? True or false: the angle of incidence is measured between the incident ray and the mirror surface.
Turning the equal-angles rule into a calculation
We just saw that $\theta_i = \theta_r$ from the normal. That raises a question: a problem often gives you the angle a ray makes with the mirror surface, not with the normal, so how do you get the angle of reflection? This card answers it → convert to the normal first, then apply the law.
If you are told the angle a ray makes with the surface, subtract it from $90°$ to get the angle from the normal, then the reflected angle is just the same value.
Because the normal is at $90°$ to the surface, the angle from the surface and the angle from the normal always add to $90°$:
$$\theta_i = \theta_r \qquad\qquad \theta_{\text{from normal}} = 90° - \theta_{\text{from surface}}$$
A ray of light strikes a plane mirror, making an angle of $25°$ with the mirror surface. Find the angle of reflection (measured from the normal).
Always measure from the normal. If a ray makes angle $\alpha$ with the surface, the angle from the normal is $90° - \alpha$. Then the angle of reflection equals the angle of incidence: $\theta_r = \theta_i$.
Add the highlighted conversion-and-rule to your notes before the check below.
Quick check: A ray hits a mirror at an angle of incidence of $40°$ from the normal. What is the angle of reflection?
Pattern A, Construct then reason
A ray strikes a plane mirror at an angle of incidence of $35°$ from the normal. In your book: (1) draw the mirror, the normal and the incident ray; (2) draw the reflected ray and label both angles; (3) state the angle of reflection and explain in one sentence which line you measured both angles from and why.
Fill the gaps: Complete the statement of the law of reflection, then press Check.
Angles in reflection are always measured from the , a line drawn at right angles to the surface. The law of reflection states that the angle of incidence equals the angle of . Both rays and the normal lie in the same .
Dot point: Describe examples of the law of reflection
Two ways to draw the same reflected wave, plus why some surfaces form images and others do not
We just learned to calculate reflected angles with rays. That raises a question: a single ray is a useful arrow, but a real wave is spread out, how do we show the whole wave reflecting, and why can you see yourself in a mirror but not in a brick wall? This card answers it → wavefront diagrams and the difference between specular and diffuse reflection.
A ray is an arrow showing the direction the wave travels; a wavefront is a line of crests drawn at right angles to the rays, both describe the same reflected wave, and whether you see a clear image depends only on how smooth the surface is.
In a linear wavefront diagram, the wavefronts (lines of crests) approach the mirror, reflect, and travel away with the wavefronts still perpendicular to the rays. A flat, smooth surface gives specular reflection: parallel incoming rays stay parallel after reflecting, so a clear image forms. A rough surface gives diffuse reflection: each point still obeys $\theta_i = \theta_r$, but because the surface faces many directions the rays scatter and no image forms.
This is why a still lake mirrors the sky (specular) but a page of paper does not (diffuse), even though both surfaces obey exactly the same law of reflection at every point.
A ray shows direction; a wavefront is a line of crests perpendicular to the rays, both describe the same reflected wave. Smooth surfaces give specular reflection (clear image); rough surfaces give diffuse reflection (scattered rays, no image), yet every point still obeys $\theta_i = \theta_r$.
Pause, copy the highlighted distinction into your book before the check below.
Last check: Decide if the statement is true or false.
Diffuse reflection from a rough surface still obeys the law of reflection at every individual point.
Match them up: Match each diagram feature to what it represents.
Dot point: Use linear wavefront diagrams and ray diagrams to analyse the motion of a wave
A fresh set drawn from this lesson's question bank, feedback shown immediately. +5 XP per correct · +25 XP all correct
Pick your answer, then rate your confidence, that tells the system what to drill next.
UnderstandBand 4(4 marks) 1. A beam of light strikes a smooth plane mirror, making an angle of $30°$ with the mirror surface. State the law of reflection, calculate the angle of reflection measured from the normal, and explain why a smooth mirror forms a clear image while a sheet of paper does not.
1 mark: states $\theta_i = \theta_r$ measured from the normal · 1 mark: converts $90° - 30° = 60°$ from the normal · 1 mark: angle of reflection $= 60°$ · 1 mark: smooth = specular (parallel rays, image); paper = diffuse (scattered rays, no image)
ApplyBand 4(3 marks) 2. A ray of light strikes a plane mirror so that it makes an angle of $25^\circ$ with the mirror surface. Determine the angle of incidence and the angle of reflection, and explain why measuring from the surface rather than the normal is a common error.
1 mark: angle of incidence $= 65^\circ$ · 1 mark: angle of reflection $= 65^\circ$ · 1 mark: explains that angles in reflection are defined from the normal, so a surface angle must be subtracted from $90^\circ$
Dot point: Describe examples of the law of reflection
AnalyseBand 5(3 marks) 3. A parallel beam of light strikes a smooth mirror and then an identical mirror that has been roughened. Using ray diagrams in your explanation, account for the difference in what is seen, and state whether the law of reflection is obeyed in both cases.
1 mark: smooth surface, all normals parallel so reflected rays stay parallel, giving a clear image · 1 mark: rough surface, normals point in many directions so reflected rays scatter · 1 mark: states the law of reflection holds at every point in both cases
Dot point: Use linear wavefront diagrams and ray diagrams to analyse the motion of a wave
MC answers and full explanations are shown inline as you complete each question. Use the retry button to attempt a fresh set from the lesson bank.
Q1 (4 marks): The law of reflection states that the angle of incidence equals the angle of reflection, $\theta_i = \theta_r$, with both angles measured from the normal (the line perpendicular to the surface). The ray makes $30°$ with the surface, so the angle from the normal is $90° - 30° = 60°$; therefore the angle of reflection is also $60°$. A smooth mirror produces specular reflection, parallel incident rays stay parallel after reflecting, so a clear image forms. A sheet of paper is rough, so it produces diffuse reflection: although every point still obeys $\theta_i = \theta_r$, the surface faces many directions and the rays scatter, so no image is formed.
Q2 (3 marks): Angles in reflection are defined between the ray and the normal, the construction line drawn perpendicular to the mirror at the point of incidence, not between the ray and the surface itself. A ray making $25^\circ$ with the surface therefore makes $90^\circ - 25^\circ = 65^\circ$ with the normal, so the angle of incidence is $65^\circ$. By the law of reflection the angle of reflection equals the angle of incidence, so it is also $65^\circ$. The error is common because the mirror surface is the visible, physical line in the diagram while the normal has to be constructed, so it is tempting to measure from what is already drawn. Using the surface angle gives $25^\circ$, which is the complement of the correct answer, and every subsequent step is then wrong by the same amount.
Q3 (3 marks): On the smooth mirror every point of the surface has a normal pointing in the same direction, so every incoming ray of the parallel beam meets its normal at the same angle of incidence and is reflected through the same angle. The reflected rays therefore remain parallel to one another, the wavefronts stay flat, and a clear image is formed: this is specular reflection. On the roughened surface the microscopic facets are tilted in many different directions, so the normals point in many different directions. Each ray still obeys the law at the point where it lands, but because the normals differ, the reflected rays leave at many different angles and the beam is scattered in all directions: this is diffuse reflection, and no image is formed. Crucially, the law of reflection is obeyed in both cases. The difference is not in the physics of each individual reflection but in the geometry of the surface, which determines whether the set of normals is uniform or varied.
You can now apply $\theta_i = \theta_r$ from the normal, draw ray and wavefront diagrams, and explain specular versus diffuse reflection. Next lesson uses the same normal-and-angle method to investigate refraction, what happens when a wave bends on entering a new medium.
↩ Back to focus-area hubAt the start you predicted where the reflected beam goes and from which line the angle is measured. The key idea is that both angles are measured from the normal, and the angle of reflection equals the angle of incidence. If you measured from the mirror surface instead, revisit Card 1, the normal is always the reference line.
A short spaced-retrieval set, mixing this lesson with earlier ones. It gets harder to guess and easier to remember.
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