Physics Q4: LESSON: Reflection, Refraction, Interference & Diffraction of Waves

LESSON: Reflection, Refraction, Interference, and Diffraction of Waves

When mechanical waves strike a barrier, at least part of the energy of the waves will be reflected back into the media from which they came. You experience this every single day, when you look in the mirror and see your own reflection.

Reflection of Mechanical Waves

When a wave strikes an obstacle or comes to the end of the medium it is traveling in, some portion of the wave is reflected back into the original medium. It reflects back at an equal angle that it came in. These angles are called the angle of incidence and the angle of reflection. The normal line, the incident and reflected rays, and the angles of incidence and reflection are all shown in the diagram sketched above. The law of reflection states that the angle of incidence equals the angle of reflection. These rules of reflection apply in the cases of water waves bouncing off the side of a pool, sound waves echoing off a distant cliff, or wave pulses traveling down a rope or a slinky.

Consider the change that would occur with a light rope joined to a heavier rope. When a wave pulse travels down the rope and encounters the media change, a reflection will occur. Look at the image below. In the top sketch, we see a lightweight (black) rope attached to a heavier rope (red). There is a wave pulse traveling down the rope from left to right. When the wave pulse encounters the barrier (the change in rope weight), part of the wave moves into the new medium and part of the wave is reflected back into the old medium.

As you can see in the bottom half of the diagram, the transmitted portion of the wave continues into the new medium right side up. The transmitted wave is somewhat diminished because some of the energy of the wave was reflected and also because the rope to be lifted is heavier. The reflected wave is also diminished because some of the energy was transmitted through the barrier. The reflected wave is also inverted (upside down). This is a general rule for mechanical waves passing from a less dense medium into a more dense medium, that is, the reflected wave will be inverted.

The situation changes when the wave is passing from a more dense medium into a less dense medium. As you can see in the sketch below, when a wave pulse moving in denser medium encounters a media interface to a medium of less density, the reflected wave is upright rather than inverted.

It is also possible for a mechanical wave to encounter an impenetrable barrier, that is, a barrier which does not allow any transmission at all. In such a case, the complete wave pulse will be reflected and the reflected wave will be inverted.

Summary

When a wave strikes an obstacle or comes to the end of the medium it is traveling in, some part of the wave is reflected back into the original medium.
The law of reflection states that the angle of incidence equals the angle of reflection.
The general rule, for mechanical waves passing from a less dense medium into a more dense medium, the reflected wave will be inverted.
When a wave pulse moving in denser medium encounters a media interface to a medium of lesser density, the reflected wave is upright rather than inverted.
When a mechanical wave encounters an impenetrable barrier, the complete wave pulse will be reflected and the reflected wave will be inverted.

Practice

The following video shows a wave machine in action. Use this video to answer the questions that follow.

What happens to the wave when it is reflected from an open end?
What happens to the wave when it is reflected from a fixed end?

A straw in a glass of water seen from the side often appears broken, even though it is not. The apparent break is due to the bending of light rays leaving the straw; as the light passes from the water to the glass and from the glass to the air, the light rays are bent. Nonetheless, your eye traces the light ray backward as if the light has followed a straight path from its origin at the straw. Since the light appears to have come from a different place, your eye sees the straw as being broken.

Refraction of Mechanical Waves

When any wave strikes a boundary between media, some of the energy is reflected and some is transmitted. When the wave strikes the media interface at an angle, the transmitted wave will move in a slightly different direction than the incident wave. This phenomenon is known as refraction.

Consider the image sketched above. Suppose that the waves represented here are water waves. The wave crests are represented by the black lines in the image. As such, the distance between two consecutive black lines is the wavelength. Let the red line represent a transition from deep to shallow water. This transition is called the media interface. As the waves hit the boundary, the waves slow down. The right side of the wave reaches the boundary before the left side of the wave, causing the left side to catch up and the angle of propagation to change slightly. This change in direction can be seen in the yellow line, which is slightly angled at the boundary.

The refraction of waves across boundaries operates similarly to the method by which tanks are steered. Tanks do not have a steering wheel. Instead, they have an accelerator to produce forward motion and separate brakes on each tread. The operator uses brakes on both treads at the same time in order to stop, but brakes on only one tread to turn the tank. By braking one side, the operator causes that side to slow down or stop while the other side continues at the previous speed, causing the tank to turn towards the slower tread.

This sketch shows a wave ray striking an interface between old medium and new medium. A normal line has been drawn as a dotted line perpendicular to the interface. The angle between the incident ray and the normal line is called the angle of incidence, shown as θi, and the angle between the refracted ray and the normal line is called the angle of refraction, θr.

We already understand that the change in the wave direction at the border depends on the difference between the two velocities. This relationship is conveniently expressed in a mathematical relationship:

$\frac{\sin\theta_r}{\sin\theta_i}=\frac{v_r}{v_i}=\frac{\lambda _r}{\lambda _i}$

The ratio of the sine of the angle of refraction to the sine of the angle of incidence is the same as the ratio of the velocity of the wave in the new medium to the velocity of the wave in the old medium and equal to the ratio of wavelength (λ) in the old medium to the wavelength in the new medium.

Example Problem: A water wave with a wavelength of 3.00 m is traveling in deep water at 16.0 m/s. The wave strikes a sharp interface with shallow water with an angle of incidence of $53.0^\circ$ . The wave refracts into the shallow water with an angle of refraction of $30.0^\circ$ . What is the velocity of the wave in shallow water and what is its wavelength in the new medium?

Solution: $\frac{\sin\theta_r}{\sin\theta_i}=\frac{v_r}{v_i}$ so $\frac{\sin30^\circ }{\sin53^\circ}=\frac{v_r}{16.0 \ m/s}$ and $v_r=10.0 \ m/s$ .

$\frac{v_r}{v_i}=\frac{\lambda _r}{\lambda _i}$ so $\frac{10.0 \ m/s}{16.0 \ m/s}=\frac{\lambda _r}{3.00 \ m}$ and $\lambda _r=1.88 \ m$ .

Example Problem: The ratio of the $\sin\theta _r$ to $\sin\theta _i$ is 0.769 . If the wavelength of a wave in a new medium is $5.00 \times 10^{-9} \ m$ , what is its wavelength in the original medium?

Solution:

$0.769=\frac{\lambda _r}{\lambda _i} \ so \ \lambda _i=\frac{5.00\times10^{-9} \ m}{0.769}=6.50\times10^{-9} \ m$

Summary

When any wave strikes a boundary between media, some of the energy is reflected and some is transmitted.
When a wave strikes the media interface at an angle, the transmitted wave will move in a different direction than the incident wave. This phenomenon is known as refraction.
At any media interface, $\frac{\sin\theta_r}{\sin\theta_i}=\frac{v_r}{v_i}=\frac{\lambda _r}{\lambda _i}$

Vocabulary

Reflection is when a wave hits a boundary, and some or all of it bounces back.
Refraction is when a wave moves into a new medium, and bends slightly
Interference is when two waves combine, either to add to each other (constructive interference) or to cancel each other out (destructive interference).
Diffraction is when a wave bends around a barrier.

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Last modified: Wednesday, 23 March 2016, 9:59 AM