E3.7 · Explain qualitative and quantitative factors in refraction

Ontario Grade 10 Science

Physics: Light and Geometric Optics

Qualitative patterns and quantitative predictions

What you will learn

• Describe refraction and identify when a transmitted ray bends toward or away from the normal.
• Explain how the starting and ending materials and the incoming angle affect refraction.
• Use refractive index and Snell’s law to predict a refracted angle when light is transmitted into the second material.
• Recognize that a ray entering along the normal changes speed but not direction.

1. Grade 9 bridge: rays, reflection, and refraction

• Refraction is a change in direction as light passes between materials.
• Measure the angles from the normal, which is at 90° to the boundary.
• The incoming ray is also called the incident ray.

2. The observable pattern: toward or away from the normal

• When transmitted into a slower-travelling material, light bends toward the normal.
• When transmitted into a faster-travelling material, light bends away from the normal.
• At 0° incidence, the ray keeps its direction across the boundary.
• The direction rule applies to a ray that is transmitted into the second material.

3. A number model: refractive index and Snell’s law

• A larger refractive index means light travels more slowly in that material.
• Use the starting and ending material in the correct places.
• Snell’s law predicts the angle of a transmitted ray.

4. Use the model and evidence carefully

• Use consistent angle measurements and identify the materials.
• The examples use hypothetical values, not measured results.
• Follow classroom directions and never look into a bright light source.

Qualitative direction changes when light is transmitted

Worked example

Predict a ray entering water

1. Identify the materials
   Air is material 1, where the ray starts. Water is material 2. Since the ray is transmitted into a material with a larger refractive index, it should bend toward the normal.
2. Substitute the known values
   Use Snell’s law, placing the incidence angle with the starting material.
   $$1.00\sin 40^\circ=1.33\sin\theta_2$$
3. Solve for the angle
   Divide by the second refractive index, then use inverse sine. Set the calculator to degree mode.
   $$\theta_2=\sin^{-1}\left(\frac{1.00\sin 40^\circ}{1.33}\right)\approx28.9^\circ$$

Worked example

Compare two incoming angles

1. Keep the material pair the same
   Both rays start in air and enter glass. Only the incoming angle changes, so the comparison shows the effect of that factor.
   $$1.00\sin\theta_1=1.50\sin\theta_2$$
2. Calculate the first angle
   Use the incidence angle of $30^\circ$, divide its sine by 1.50, and take inverse sine.
   $$\theta_2=\sin^{-1}\left(\frac{\sin 30^\circ}{1.50}\right)\approx19.5^\circ$$
3. Calculate the second angle
   Repeat the calculation with an incidence angle of $60^\circ$. The refracted angle is larger than in the first case, but remains smaller than its incidence angle.
   $$\theta_2=\sin^{-1}\left(\frac{\sin 60^\circ}{1.50}\right)\approx35.3^\circ$$

Worked example

Light entering along the normal

1. Read the geometry
   A ray travelling along the normal has an angle of $0^\circ$ from the normal. Its direction will not change as it crosses the boundary.
   $$\theta_1=0^\circ$$
2. Apply the relationship
   The sine of $0^\circ$ is zero. Snell’s law therefore gives a refracted angle of $0^\circ$ as well.
   $$1.00\sin 0^\circ=1.40\sin\theta_2$$

Common mistakes and how to avoid them

Lesson summary

• Refraction is a change in the direction of light as it passes between materials.
• Angles of incidence and refraction are measured from the normal.
• When transmitted into a slower-travelling material, a ray bends toward the normal; when transmitted into a faster-travelling material, it bends away.
• The materials and incidence angle affect the refracted angle. Snell’s law gives a quantitative prediction for a transmitted ray.
• At normal incidence, the direction stays the same even though the speed changes.

Check your understanding

Key terms

Refraction

The change in direction of light as it passes between materials.

Ray

A model line showing the direction in which light travels.

Boundary

The surface where two materials meet.

Normal

An imaginary line at 90° to a boundary.

Angle of incidence

The angle between the incoming ray and the normal.

Angle of refraction

The angle between a transmitted ray and the normal.

Refractive index

A number that describes how much a material slows light compared with a vacuum.

Snell’s law

The relationship used to connect refractive indices and the angles of incidence and refraction.

Continue through SNC2D

View the complete SNC2D Ontario Grade 10 Science curriculum and lessons

• E3.6 · Connect mirror and lens properties to optical instruments
• E3.8 · Explain natural optical effects with light properties
• E1.1 · Evaluate a technology that alters human perception of light
• E1.2 · Explain societal benefits of an optical device
• E2.1 · Use optics terms including incidence, focus, and virtual image
• E2.2 · Investigate reflection with plane and curved mirrors and ray diagrams

About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 10 Science (SNC2D), expectation E3.7. 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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