C.3.1 Reflection, refraction, and diffraction

Wave Propagation: Reflection, Refraction, and Diffraction

Waves exhibit unique behaviors when they encounter obstacles or boundaries.

Reflection, refraction, and diffraction are three fundamental phenomena that reveal the wave nature of light and other types of waves.

Wavefronts and Rays: Visualizing Wave Propagation

To understand how waves propagate, physicists use two complementary concepts: wavefronts and rays.

These tools help us visualize the direction and behavior of waves in two and three dimensions.

Wavefronts

Definition

Wavefront

A wavefront is an imaginary surface that connects points on a wave that are in phase (i.e., at the same point in their oscillation cycle).

Wavefronts are often depicted as lines or surfaces:

In two dimensions, wavefronts appear as lines (e.g., concentric circles for ripples on water).
In three dimensions, wavefronts form surfaces (e.g., spherical shells for sound waves).

Example

Imagine a pebble dropped into a pond.
The wavefronts are the circular ripples that spread outward, representing points where the water surface is at the same height.

Rays

Definition

Ray

A ray is a line drawn perpendicular to a wavefront, indicating the direction of wave propagation.

Rays are useful for visualizing how waves travel and interact with obstacles.

Example

In the case of light waves, rays show the path that light takes as it travels, reflects, or refracts.

Using Wavefronts and Rays Together

Wavefronts and rays provide complementary information:

Wavefronts show the shape and phase of the wave.
Rays indicate the direction of energy transfer.

Tip

When drawing wavefronts and rays, remember that rays are always perpendicular to the wavefronts.

Reflection: Waves Bouncing Off Surfaces

Definition

Reflection

Reflection occurs when a wave strikes a surface and bounces back into the original medium.

This behavior is governed by the law of reflection, which states that the angle of incidence is equal to the angle of reflection.

Note

The angle of incidence is the angle between the incoming wave and the normal (a line perpendicular to the surface).

The angle of reflection is the angle between the reflected wave and the normal.

How Reflection Works

Imagine a beam of light hitting a mirror.
The light wave approaches the mirror at a certain angle, called the angle of incidence.
Upon striking the mirror, the wave reflects off the surface at an angle equal to the angle of incidence.

Tip

Reflection occurs in many types of waves, including light, sound, and water waves.
The smoothness of the surface determines the quality of the reflection.
A smooth surface, like a mirror, produces a clear reflection, while a rough surface scatters the waves in different directions.

Refraction: Change in Wave Direction

Definition

Refraction

Refraction is the bending of a wave as it passes from one medium to another, caused by a change in the wave’s speed.

This phenomenon is most commonly observed in light waves but applies to all types of waves, including sound and water waves.

Why Does Refraction Happen?

When a wave enters a new medium, its speed changes.
If the wave enters at an angle, this change in speed causes the wave to bend.

Example

Consider a light wave moving from air into water. In air, the wave travels faster than in water. As the wave enters the water, the part of the wavefront that hits the water first slows down, causing the entire wave to bend toward the normal.

Snell’s Law: The Mathematical Rule of Refraction

Snell’s Law quantifies the relationship between the angles of incidence and refraction and the speeds of the wave in the two media.
It is expressed as:

$\frac{n_{1}}{n_{2}} = \frac{\sin θ_{2}}{\sin θ_{1}} = \frac{v_{2}}{v_{1}}$

where:

$n_{1}$ and $n_{2}$ are the refractive indices of the two media.
$θ_{1}$ and $θ_{2}$ are the angles of incidence and refraction, respectively.
$v_{1}$ and $v_{2}$ are the wave speeds in the respective media.

Definition

Refractive index

The refractive index ( $n$ ) of a medium is a measure of how much the wave slows down in that medium compared to a vacuum.

Hint

A higher refractive index indicates a slower wave speed.

Example question

Calculating the angle of refraction

A light wave enters water from air at an angle of $30^{\circ}$ . The refractive index of air is approximately $1.0$ , and that of water is $1.33$ .

What is the angle of refraction?

Solution

Using Snell’s Law:

$n_{1} \sin θ_{1} = n_{2} \sin θ_{2}$

Substitute the known values:

$1.0 \cdot \sin 30^{\circ} = 1.33 \cdot \sin θ_{2}$

Solve for $\sin θ_{2}$ :

$\sin θ_{2} = \frac{\sin 30^{\circ}}{1.33} \approx 0.376$

Therefore, $θ_{2} \approx 22^{\circ}$ .

Tip

When a wave moves from a less dense to a more dense medium (e.g., air to water), it bends toward the normal.
Conversely, when it moves from a more dense to a less dense medium, it bends away from the normal.

Diffraction: Bending Around Obstacles

Definition

Diffraction

Diffraction is the spreading of waves as they pass through an aperture or around an obstacle.

This phenomenon is most pronounced when the size of the aperture or obstacle is comparable to the wavelength of the wave.

How Diffraction Works

Imagine water waves approaching a narrow gap in a barrier.
As the waves pass through the gap, they spread out in circular patterns.
The smaller the gap relative to the wavelength, the more pronounced the diffraction.

Example

Diffraction explains why you can hear sound around a corner but cannot see around it.
Sound waves have longer wavelengths than light waves, allowing them to diffract more easily around obstacles.

Factors Affecting Diffraction

Wavelength: Longer wavelengths diffract more than shorter wavelengths.
Aperture Size: Diffraction is more significant when the aperture size is similar to the wavelength.

Common Mistake

Students often confuse diffraction with refraction.

Remember, diffraction occurs when waves bend around obstacles or through openings, while refraction involves bending due to a change in speed across media.

Summary

Reflection, refraction, and diffraction are fundamental wave phenomena that reveal the unique behaviors of waves.

Reflection involves waves bouncing off surfaces, following the law of reflection.
Refraction is the bending of waves due to a change in speed across media, described by Snell’s Law.
Diffraction is the spreading of waves around obstacles or through apertures, most pronounced when the wavelength is comparable to the obstacle size.

Self review

Can you explain how Snell’s Law relates the angles of incidence and refraction to the refractive indices of two media?
How does diffraction differ from refraction?

Theory of Knowledge

How do the principles of reflection, refraction, and diffraction influence the design of technologies we use every day?
Consider how these wave behaviors might be applied in future innovations.

These concepts are not only essential for understanding wave behavior but also have practical applications in fields like optics, radar, and acoustics.

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C.3.1 Reflection, refraction, and diffraction

Wave Propagation: Reflection, Refraction, and Diffraction

Wavefronts and Rays: Visualizing Wave Propagation

Wavefronts

Rays

Using Wavefronts and Rays Together

Reflection: Waves Bouncing Off Surfaces

How Reflection Works

Refraction: Change in Wave Direction

Why Does Refraction Happen?

Snell’s Law: The Mathematical Rule of Refraction

Calculating the angle of refraction

Diffraction: Bending Around Obstacles

How Diffraction Works

Factors Affecting Diffraction

Summary

You've read 2/2 free chapters this week.

Introduction to Wave Propagation