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E3.4 · Explain partial and total internal reflection with ray diagrams

Learn to explain partial and total internal reflection with ray diagrams through clear examples and targeted practice.

Ontario Grade 10 Science

Physics: Light and Geometric Optics

How light behaves at a boundary between two materials

Have you seen light reflected inside a clear glass object or a stream of water? At a boundary, light can reflect, pass into the next material, or do both. A ray diagram helps show these paths. In this lesson, you will use a simple model to explain partial reflection and total internal reflection. The focus is on what happens to light at the boundary, not on calculating a critical angle.

What you will learn

Describe what happens when light reaches a boundary between materials.
Use ray diagrams to show partial and total internal reflection.
Identify the conditions needed for total internal reflection.

1. Grade 9 bridge: light and boundaries

Light travels in straight lines through a uniform material. A ray is a simple line with an arrow that represents the direction light travels. A boundary is the surface where one material meets another, such as the surface between water and air.

When a ray reaches a boundary, it may reflect. Reflection means that light bounces back into the material it came from. Light may also pass through the boundary and change direction. This change in direction is called refraction. At many boundaries, some light reflects and some refracts.

To draw the paths clearly, draw a normal at the point where the ray meets the boundary. The normal is an imaginary line at right angles to the surface. Measure the angles between each ray and the normal, not between a ray and the surface.

\theta_i=\theta_r

A ray represents the direction light travels.
Reflection sends light back into its original material.
Refraction is a change in direction as light passes into another material.
The normal is perpendicular to the boundary.

2. What partial reflection looks like

Imagine shining a narrow beam of light from water toward the water–air surface. In the usual case, part of the light reflects back into the water. The rest passes into the air and refracts. This is partial reflection: only part of the incoming light is reflected.

In a ray diagram, draw the boundary as a straight line and the normal through the point where the incoming ray reaches it. Draw the incoming ray with its arrow pointing toward the boundary. Then draw a reflected ray back into the first material. Draw a refracted ray into the second material. The reflected and refracted rays represent different parts of the light.

The law of reflection says that the angle of reflection equals the angle of incidence. The angle of incidence is the angle between the incoming ray and the normal. The angle of reflection is the angle between the reflected ray and the normal. The reflected path is therefore a mirror image of the incoming path across the normal.

A ray diagram shows directions, not how much light travels along each path. Do not conclude that the reflected and refracted parts are equal in brightness just because both rays are drawn.

\theta_i=\theta_r

Partial reflection has both a reflected ray and a refracted ray.
The angles are measured from the normal.
The reflected ray makes the same angle with the normal as the incoming ray.

3. When reflection becomes total

Total internal reflection is different. It happens only when light is travelling in a material where light travels more slowly and reaches a boundary with a material where light travels faster. For example, light can travel from water toward air. The direction of travel matters: light going from air toward water does not meet this condition.

As the incoming ray in the first material approaches the boundary more steeply, its angle from the normal increases. At one particular angle, called the critical angle, the refracted ray travels along the boundary. The critical angle is the angle of incidence that produces this along-the-boundary refracted ray.

If the angle of incidence becomes larger than the critical angle, no refracted ray passes into the second material in this model. All the incoming light is reflected back into the first material. This is total internal reflection. A ray diagram for this case shows the incoming ray and reflected ray on the same side of the boundary, with no outgoing refracted ray.

Do not confuse a ray that runs along the boundary at the critical angle with total internal reflection. At the critical angle, the ray is along the boundary. Total internal reflection occurs when the angle is greater than the critical angle and the light stays in the first material.

\theta_i>\theta_c

Light must travel from a material where it travels more slowly to one where it travels faster.
At the critical angle, the refracted ray runs along the boundary.
Above the critical angle, all the light is reflected back into the first material.

4. Read and check a ray diagram

A useful ray diagram includes the boundary, the normal, the incoming ray, and the correct outgoing path or paths. Label the materials on both sides. Mark the angle from the normal when an angle is given. For partial reflection, include both a reflected and refracted ray. For total internal reflection, include only the reflected ray as the outgoing path.

The diagram is a model. It helps you track the paths of light, but it is not a photograph and does not show the amount of light in each path. A real observation can support the model when it shows a reflected path, a transmitted path, or the change from both paths to reflection only under the required conditions.

In a classroom investigation, follow the teacher’s directions for any light source or optical equipment. Never shine a bright beam, including a laser, into anyone’s eyes. Do not look directly into a beam or its reflection.

Check the direction of travel and identify both materials before deciding which model applies.
Use the normal to compare angles.
Keep the critical-angle case separate from the greater-than-critical-angle case.

Compare the boundary cases

Situation	What the ray diagram shows
Partial reflection	A reflected ray and a refracted ray
At the critical angle	A reflected ray and a refracted ray along the boundary
Above the critical angle, with light travelling from slower to faster	A reflected ray only; no refracted ray into the second material

Worked example

Partial reflection at a boundary

A ray travels from water toward air and strikes the surface at an incidence angle of 32°. Describe the paths to draw for a partial-reflection case. Do not assume a critical angle value.

Identify the paths
The problem describes partial reflection, so the diagram must show light both returning to the water and passing into the air. Draw a horizontal boundary, label water below it and air above it, and add a normal at the point where the ray hits.
Apply the reflection rule
Measure the incidence angle from the normal. The reflected ray stays in the water and makes the same angle with the normal as the incoming ray. Draw the refracted ray in the air as a separate path; no refracted angle was supplied, so do not invent a number for it.
$\theta_r=32^\circ$

Answer: Draw an incoming ray in water, a reflected ray in water at 32° to the normal, and a refracted ray in air. The 32° value specifies the reflected angle, not the refracted angle.

Check: Both outgoing paths are needed for partial reflection, and the reflection angle is measured from the normal.

Worked example

Recognize the critical-angle case

A ray travels from a material where light travels more slowly into one where light travels faster. Its incidence angle is exactly the critical angle. What should its ray diagram show?

Check the direction
The ray travels from the material where light travels more slowly to one where it travels faster. This is the direction required for the critical-angle model.
Draw the boundary path
At the critical angle, the refracted ray travels along the boundary. The reflected ray also remains in the first material and follows the law of reflection. Do not label this as total internal reflection, because the incidence angle is not greater than the critical angle.
$\theta_i=\theta_c$

Answer: Show a refracted ray along the boundary, as well as a reflected ray in the original material.

Check: Equality with the critical angle gives a ray along the boundary; total internal reflection requires a larger incidence angle.

Worked example

Decide whether reflection is total

Light travels from a material where it travels more slowly to one where it travels faster. In a hypothetical case, the incidence angle is 48° and the critical angle is 41°. Decide what outgoing path to draw.

Compare the angles
The ray is travelling in the required direction. Compare its incidence angle with the critical angle: 48° is greater than 41°.
$48^\circ>41^\circ$
Choose the path
Because the incidence angle is greater than the critical angle, the ray undergoes total internal reflection. Draw the reflected ray in the original material, at the same angle from the normal as the incoming ray. Do not draw a refracted ray into the second material.
$\theta_r=48^\circ$

Answer: Draw only the reflected outgoing ray in the original material. Its reflection angle is 48°.

Check: The hypothetical values satisfy the greater-than condition, and the reflection rule sets the reflected angle equal to the incidence angle.

Common mistakes and how to avoid them

Measuring an angle from the boundary.

Correction: Measure the angle between the ray and the normal, which is perpendicular to the boundary.

Drawing only a reflected ray for every boundary.

Correction: For partial reflection, show both the reflected ray and the refracted ray.

Calling the critical-angle case total internal reflection.

Correction: At the critical angle, the refracted ray runs along the boundary. Total internal reflection occurs above that angle.

Assuming total internal reflection can happen in either direction across a boundary.

Correction: Check that light is travelling from the material where it travels more slowly toward the material where it travels faster.

Lesson summary

At a boundary, light may reflect, refract, or do both.
For partial reflection, draw both a reflected ray and a refracted ray.
The angle of reflection equals the angle of incidence, measured from the normal.
At the critical angle, the refracted ray travels along the boundary.
When light travels in the required direction and its incidence angle is greater than the critical angle, total internal reflection occurs.

Check your understanding

Question 1

A ray has an incidence angle of 27°. What is its reflection angle?

27° from the normal
63° from the normal
0° from the normal
27° from the boundary

Show answer and explanation

27° from the normal

The reflection angle equals the incidence angle. Both angles are measured from the normal.

Question 2

At the critical angle, which description is correct?

The refracted ray travels along the boundary.
The refracted ray always returns into the original material.
The incoming ray stops at the boundary.
The reflected ray passes into the second material.

Show answer and explanation

The refracted ray travels along the boundary.

The critical angle is the incidence angle that makes the refracted ray run along the boundary.

Question 3

Which case shows total internal reflection?

Light travels in the required slower-to-faster direction, and its incidence angle is greater than the critical angle.
Light travels in the required direction, and its incidence angle is below the critical angle.
Light travels from the faster-light material toward the slower-light material, at any angle.
The incidence angle equals the critical angle, so the refracted ray is absent.

Show answer and explanation

Light travels in the required slower-to-faster direction, and its incidence angle is greater than the critical angle.

Both the direction of travel and an incidence angle greater than the critical angle are required. At the critical angle, a refracted ray still runs along the boundary.

Key terms

Ray: A line with an arrow that represents the direction light travels.
Boundary: The surface where two materials meet.
Normal: An imaginary line at right angles to a boundary at the point where a ray reaches it.
Reflection: The return of light into the material it came from after it reaches a boundary.
Refraction: A change in direction as light passes from one material into another.
Partial reflection: A case where some light reflects and some passes through the boundary.
Critical angle: The incidence angle that makes the refracted ray travel along the boundary.
Total internal reflection: The reflection of all incoming light back into the first material when the required direction and angle conditions are met.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 10 Science (SNC2D), expectation E3.4. 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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