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
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).
- Consider 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
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.
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.
When drawing wavefronts and rays, remember that rays are always perpendicular to the wavefronts.
Reflection: Waves Bouncing Off Surfaces
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.
- 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
- Consider 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.
- 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
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.
- 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: $$
\frac{n_1}{n_2} = \frac{\sin \theta_2}{\sin \theta_1} = \frac{v_2}{v_1}
$$ where:- $n_1$ and $n_2$ are the refractive indices of the two media.
- $\theta_1$ and $\theta_2$ are the angles of incidence and refraction, respectively.
- $v_1$ and $v_2$ are the wave speeds in the respective media.
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.
A higher refractive index indicates a slower wave speed.
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: $$
n_1 \sin \theta_1 = n_2 \sin \theta_2
$$ - Substitute the known values: $$
1.0 \cdot \sin 30^\circ = 1.33 \cdot \sin \theta_2
$$ - Solve for $\sin \theta_2$: $$
\sin \theta_2 = \frac{\sin 30^\circ}{1.33} \approx 0.376
$$ - Therefore, $\theta_2 \approx 22^\circ$.
- 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.
Refraction of Light
Diffraction: Bending Around Obstacles
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
- Consider 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.
- 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.
- 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.
- 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?
