3bWave Behavior: Reflection and Refraction
Master the law of reflection, apply Snell's law to refraction, and explore how waves diffract around obstacles.
Reflection and refraction are the foundation of lenses, mirrors, fiber optics, and medical imaging — understanding wave behavior at boundaries is essential for modern technology.
What happens to a wave when it encounters a boundary — and why does light bend when it enters water?
Lesson Overview
When waves encounter boundaries or obstacles, they can reflect, refract, or diffract. The law of reflection governs how waves bounce off surfaces. Snell's law describes refraction — the bending of waves as they cross from one medium to another at different speeds. Diffraction explains how waves spread around obstacles. Understanding these behaviors is essential for optics, acoustics, and telecommunications.
Key Concepts
Law of Reflection
Angle of incidence equals angle of reflection (θᵢ = θᵣ), measured from the normal
Refraction
Bending of a wave as it crosses a boundary where wave speed changes
Snell's Law
n₁ sin θ₁ = n₂ sin θ₂ — relates angles and indices of refraction at a boundary
Index of Refraction (n)
n = c/v; ratio of speed of light in vacuum to speed in the medium
Diffraction
Spreading of waves around obstacles or through openings; most pronounced when λ ≈ gap size
Wave Speed at Boundaries
Wave speed changes at a boundary; frequency stays constant; wavelength changes
Worked Examples
A ray of light strikes a flat mirror at an angle of incidence of 35°. What is the angle of reflection?
Light travels from air (n₁ = 1.00) into glass (n₂ = 1.50) at an angle of incidence of 30°. Find the angle of refraction.
Light travels from glass (n = 1.50) into water (n = 1.33) at 25°. Find the refracted angle.
Explain why a straw appears bent when placed in a glass of water.
Sound waves with wavelength 0.50 m pass through a doorway 0.60 m wide. Will significant diffraction occur? Explain.
Guided Problems
A light ray hits a mirror at 50° to the surface (not the normal). What is the angle of reflection measured from the normal?
Hint: The angle of incidence is measured from the normal, not the surface. If the ray is 50° from the surface, it is 90° − 50° = 40° from the normal.
Light passes from water (n = 1.33) into air (n = 1.00) at 20°. Use Snell's law to find the refracted angle.
Hint: Apply n₁ sin θ₁ = n₂ sin θ₂. Solve for sin θ₂ then take the inverse sine.
Why does a fish in a pond appear shallower than it actually is?
Hint: Think about how light from the fish refracts as it exits the water into air — does it bend toward or away from the normal?
Radio waves (λ ≈ 1 m) diffract around buildings, but visible light (λ ≈ 500 nm) does not. Explain why.
Hint: Compare the wavelength to the size of the obstacle. Diffraction is significant when λ ≈ obstacle size.
When a wave crosses a boundary from a fast medium to a slow medium, does it bend toward or away from the normal?
Hint: Use Snell's law: if v decreases, n increases, so sin θ₂ < sin θ₁, meaning θ₂ < θ₁.
Key Vocabulary
Law of Reflection
The angle of incidence equals the angle of reflection, both measured from the normal to the reflecting surface.
Example: A mirror reflects a laser beam at the same angle it arrives — θᵢ = θᵣ.
Refraction
The bending of a wave as it passes from one medium to another where its speed changes.
Example: A pencil in a glass of water appears bent because light refracts at the water–air boundary.
Snell's Law
n₁ sin θ₁ = n₂ sin θ₂ — the relationship between angles and indices of refraction at a boundary.
Example: Light entering glass from air bends toward the normal because glass has a higher index of refraction.
Diffraction
The spreading of waves around obstacles or through openings; most significant when the wavelength is comparable to the obstacle or gap size.
Example: Sound diffracts around corners, which is why you can hear someone talking in the next room even without line of sight.
Interactive Practice — 5 Questions
The law of reflection states that the angle of incidence equals:
Light travels from air (n=1.00) into diamond (n=2.42) at 30°. The refracted ray bends:
Snell's law is written as:
Diffraction is most pronounced when the wavelength is:
When a wave crosses a boundary, which property stays constant?
Independent Practice
A light ray strikes a mirror at 42° to the normal. Draw a diagram and find the angle of reflection.
Light passes from air (n = 1.00) into water (n = 1.33) at an angle of incidence of 45°. Calculate the angle of refraction.
Explain total internal reflection: what condition must be met, and give one technological application.
A wave travels from medium A (speed 400 m/s) to medium B (speed 200 m/s) at 30°. Calculate the angle of refraction using the wave form of Snell's law: sin θ₁/v₁ = sin θ₂/v₂.
★ A fiber-optic cable uses total internal reflection to transmit light. Explain how Snell's law governs this, calculate the critical angle for glass (n = 1.50) to air (n = 1.00), and describe what happens to a ray that hits the boundary at an angle greater than the critical angle.
ChallengeCommon Mistakes
Measuring the angle of incidence from the surface instead of the normal.
All angles in reflection and refraction (θᵢ, θᵣ, θ₂) are measured from the normal — the line perpendicular to the surface at the point of incidence.
Thinking refraction only applies to light.
Refraction applies to all waves — sound, water waves, and seismic waves all refract when their speed changes at a boundary.
Confusing diffraction with refraction.
Refraction is bending due to a speed change at a boundary. Diffraction is spreading around obstacles or through gaps — no boundary crossing required.
Math Tips
In Snell's law, always use the sine of the angle, not the angle itself. Use a calculator: sin⁻¹ to find the angle from its sine.
The index of refraction n = c/v is always ≥ 1 (since v ≤ c). A higher n means slower wave speed in that medium.