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E2.2 · Investigate reflection with plane and curved mirrors and ray diagrams

Learn to investigate reflection with plane and curved mirrors and ray diagrams through clear examples and targeted practice.

Ontario Grade 10 Science

Physics: Light and Geometric Optics

Using observations and ray diagrams to describe reflected light

A face appears in a bathroom mirror because light from the face reaches the mirror and reflects toward the eyes. Reflection is the change in direction of light when it meets a surface and bounces away. In this lesson, you will investigate plane and curved mirrors and use ray diagrams to represent what happens. A ray diagram is a simple model: each line shows the direction light travels, not the full beam of light.

What you will learn

Describe reflection from a plane mirror and from curved mirrors.
Use a normal and the law of reflection to draw a ray diagram.
Compare how concave and convex mirrors change the directions of reflected rays.
Use careful observations to support a conclusion about a mirror.

From straight-line light to a reflection model

A useful Grade 9 idea is that light travels in straight lines through a uniform space. A ray is a line with an arrow that represents the direction light travels. When a ray reaches a mirror, it changes direction. The incoming ray is the incident ray. The ray that leaves the mirror is the reflected ray.

A plane mirror has a flat reflecting surface. A curved mirror has a reflecting surface that bends inward or outward. A concave mirror curves inward, like the inside of a spoon. A convex mirror curves outward, like the back of a spoon. The spoon examples help you picture the shapes; a mirror is the surface being studied.

To draw a reflection, first mark the point where the ray reaches the mirror. Then draw a normal at that point. The normal is an imaginary line at a right angle to the mirror surface. Measure the ray's angle from the normal, not from the mirror surface. The angle of incidence is the angle between the incident ray and the normal. The angle of reflection is between the reflected ray and the normal.

\theta_i = \theta_r

Arrows show the direction of light travel.
The normal meets the surface at a right angle.
Measure both angles from the normal.

The law of reflection and plane mirrors

The law of reflection states that the angle of incidence equals the angle of reflection. The incident ray, reflected ray, and normal are drawn in the same flat diagram. If a ray arrives straight along the normal, its angle of incidence is zero, so it travels back along the same line in the opposite direction.

A plane mirror reflects a set of parallel incoming rays as parallel outgoing rays. The rays change direction, but they do not spread toward one another or away from one another because of the flat surface. This helps explain why a plane mirror can show a clear image of an object.

In a ray diagram, use a ruler for straight rays and put arrowheads on them. Draw the normal as a dashed or clearly different line if that helps you tell it apart from light rays. A diagram is a model of directions. It does not show every light ray in a room.

A flat mirror has the same surface direction across the point where the ray hits.
Equal angles are measured on opposite sides of the normal.
Use arrows so the direction of each ray is clear.

What changes with a curved mirror?

At each point on a curved mirror, the normal is still at a right angle to the surface at that point. The surface direction changes from place to place, so the normal changes too. Apply the law of reflection at the point where each ray meets the mirror.

A concave mirror can reflect parallel incoming rays so they head toward one another. A convex mirror can reflect parallel incoming rays so they spread apart. These are useful overall patterns to look for in ray diagrams. For an individual ray, the angle rule still applies at the contact point.

When investigating, compare rays that reach different parts of the curve. Do not assume the normal is the same everywhere on a curved surface. Draw a local normal for each contact point. This makes the diagram match the mirror's shape and helps explain why the outgoing directions differ.

A curved surface has a different normal at different points.
Concave mirrors can bring reflected parallel rays closer together.
Convex mirrors can make reflected parallel rays spread apart.

Investigating with evidence and care

A simple classroom investigation can use a plane mirror, a curved mirror, a ray box or another teacher-approved light source, paper, and a ruler. Shine a narrow ray toward the mirror and mark the incoming and outgoing directions. For a curved mirror, repeat at different points on the surface. Record what you see rather than deciding in advance what the rays must do.

A helpful record includes the mirror type, where the ray met the mirror, the direction of the incoming ray, and the direction of the reflected ray. A sketch with arrows is often clearer than a long description. Compare the sketches for a plane, concave, and convex mirror. The observations should support a claim about whether rays stay parallel, come closer together, or spread apart.

Use only equipment and light sources approved by your teacher. Never aim a bright beam, including sunlight reflected from a mirror, into anyone's eyes. Keep mirrors stable and handle glass mirrors carefully. If a mirror is damaged, tell the teacher rather than picking up broken pieces.

Change one feature at a time when comparing observations.
Record directions with labelled sketches or notes.
Protect eyes and follow classroom equipment instructions.

Mirror shape and reflected-ray pattern

Mirror	Surface shape	Pattern for parallel incoming rays
Plane	Flat	Reflected rays remain parallel
Concave	Curves inward	Reflected rays can head toward one another
Convex	Curves outward	Reflected rays can spread apart

Worked example

Reflecting from a plane mirror

A ray reaches a plane mirror at an angle of incidence of 35°. What is its angle of reflection, measured from the normal?

Identify the rule
The mirror is plane, but the law of reflection applies to a ray at the contact point on any mirror. The two angles are measured from the normal.
Set the angles equal
The angle of reflection must have the same size as the angle of incidence.
$\theta_r = 35^\circ$

Answer: The angle of reflection is 35° from the normal.

Check: The reflected ray lies on the other side of the normal from the incident ray.

Worked example

Tracing a ray on a curved mirror

At one point on a concave mirror, a ray arrives at 24° from the local normal. What angle should you draw for the reflected ray, and what must you do before drawing it?

Locate the contact point
The mirror is curved, so the normal depends on where the ray hits. Draw a normal at this particular contact point before measuring the angle.
Apply the angle rule
At that point, the angle of reflection equals the given angle of incidence. Draw the reflected ray on the opposite side of the normal.
$\theta_r = 24^\circ$

Answer: Draw the reflected ray at 24° from the local normal, on the opposite side of that normal.

Check: Using a normal from another point on the curve could give the wrong ray direction.

Worked example

Comparing curved mirrors

A set of parallel rays is directed toward a concave mirror and then toward a convex mirror. Describe the pattern to look for in the reflected rays.

Compare the surface shapes
The concave surface bends inward, while the convex surface bends outward. Their surface directions, and therefore their local normals, vary across the mirror.
Describe the ray patterns
Apply the law of reflection at each point. The overall pattern is that the concave mirror can turn parallel incoming rays toward one another, while the convex mirror can turn them so they spread apart.

Answer: Look for reflected rays that move closer together after the concave mirror and spread apart after the convex mirror.

Check: These are overall patterns. The angle of incidence still equals the angle of reflection at every contact point.

Common mistakes and how to avoid them

Measuring an angle from the mirror surface.

Correction: Draw the normal first. Measure both angles from that line.

Drawing one normal across the whole curved mirror.

Correction: Draw a separate normal at each ray's contact point because the surface direction changes.

Thinking a curved mirror has a different reflection rule.

Correction: Use the same law of reflection at each point. The changing surface direction changes the local normal.

Drawing a ray without an arrow.

Correction: Add arrowheads to show which way light travels.

Lesson summary

Reflection happens when light changes direction at a surface.
The normal is at a right angle to the mirror at the point where a ray hits.
The angle of incidence equals the angle of reflection; measure both from the normal.
Plane mirrors keep reflected parallel rays parallel. Concave and convex mirrors can make parallel rays move toward one another or spread apart.
Use observations and labelled ray diagrams to compare mirrors safely.

Check your understanding

Question 1

A ray meets a plane mirror at 42° from the normal. What is its angle of reflection?

21°
42°
48°
90°

Show answer and explanation

42°

The law of reflection says the angles are equal when both are measured from the normal.

Question 2

Why should a ray diagram for a curved mirror show a local normal?

The normal changes direction as the curved surface changes direction.
Curved mirrors do not reflect light.
The normal shows the direction the object moves.
The normal is always parallel to the mirror.

Show answer and explanation

The normal changes direction as the curved surface changes direction.

At each contact point, the normal is at a right angle to the surface there. A curved surface has different directions at different points.

Question 3

Which pattern can be observed when parallel rays reflect from a convex mirror?

They always stop at the mirror.
They can spread apart.
They remain inside the mirror.
They must meet at the same point on the surface.

Show answer and explanation

They can spread apart.

A convex mirror can reflect parallel incoming rays so they spread apart.

Key terms

Reflection: A change in the direction of light when it meets a surface and bounces away.
Ray: A line with an arrow that represents the direction light travels.
Incident ray: The ray travelling toward a reflecting surface.
Reflected ray: The ray travelling away from a reflecting surface after reflection.
Normal: An imaginary line at a right angle to the surface at the point where a ray meets it.
Plane mirror: A mirror with a flat reflecting surface.
Concave mirror: A mirror with a reflecting surface that curves inward.
Convex mirror: A mirror with a reflecting surface that curves outward.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 10 Science (SNC2D), expectation E2.2. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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