27.2 Huygens's principle: diffraction  (Page 2/4)

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The law of refraction can be explained by applying Huygens’s principle to a wavefront passing from one medium to another (see [link] ). Each wavelet in the figure was emitted when the wavefront crossed the interface between the media. Since the speed of light is smaller in the second medium, the waves do not travel as far in a given time, and the new wavefront changes direction as shown. This explains why a ray changes direction to become closer to the perpendicular when light slows down. Snell’s law can be derived from the geometry in [link] , but this is left as an exercise for ambitious readers.

What happens when a wave passes through an opening, such as light shining through an open door into a dark room? For light, we expect to see a sharp shadow of the doorway on the floor of the room, and we expect no light to bend around corners into other parts of the room. When sound passes through a door, we expect to hear it everywhere in the room and, thus, expect that sound spreads out when passing through such an opening (see [link] ). What is the difference between the behavior of sound waves and light waves in this case? The answer is that light has very short wavelengths and acts like a ray. Sound has wavelengths on the order of the size of the door and bends around corners (for frequency of 1000 Hz, $\lambda =c/f=\left(\text{330}\phantom{\rule{0.25em}{0ex}}\text{m}/\text{s}\right)/\left(\text{1000}\phantom{\rule{0.25em}{0ex}}{\text{s}}^{-1}\right)=0\text{.}\text{33 m}$ , about three times smaller than the width of the doorway).

If we pass light through smaller openings, often called slits, we can use Huygens’s principle to see that light bends as sound does (see [link] ). The bending of a wave around the edges of an opening or an obstacle is called diffraction    . Diffraction is a wave characteristic and occurs for all types of waves. If diffraction is observed for some phenomenon, it is evidence that the phenomenon is a wave. Thus the horizontal diffraction of the laser beam after it passes through slits in [link] is evidence that light is a wave.

Making connections: diffraction

Diffraction of light waves passing though openings is illustrated in [link] . But the phenomenon of diffraction occurs in all waves, including sound and water waves. We are able to hear sounds from nearby rooms as a result of diffraction of sound waves around obstacles and corners. The diffraction of water waves can be visually seen when waves bend around boats.

As shown in [link] , the wavelengths of the different types of waves affect their behavior and diffraction. In fact, no observable diffraction occurs if the wave’s wavelength is much smaller than the obstacle or slit. For example, light waves diffract around extremely small objects but cannot diffract around large obstacles, as their wavelength is very small. On the other hand, sound waves have long wavelengths and hence can diffract around large objects.

Test prep for ap courses

Which of the following statements is true about Huygens’s principle of secondary wavelets?

1. It can be used to explain the particle behavior of waves.
2. It states that each point on a wavefront can be considered a new wave source.
3. It can be used to find the velocity of a wave.
4. All of the above.

(b)

Explain why the amount of bending that occurs during diffraction depends on the width of the opening through which light passes.

Section summary

• An accurate technique for determining how and where waves propagate is given by Huygens’s principle: Every point on a wavefront is a source of wavelets that spread out in the forward direction at the same speed as the wave itself. The new wavefront is a line tangent to all of the wavelets.
• Diffraction is the bending of a wave around the edges of an opening or other obstacle.

Conceptual questions

How do wave effects depend on the size of the object with which the wave interacts? For example, why does sound bend around the corner of a building while light does not?

Under what conditions can light be modeled like a ray? Like a wave?

Go outside in the sunlight and observe your shadow. It has fuzzy edges even if you do not. Is this a diffraction effect? Explain.

Why does the wavelength of light decrease when it passes from vacuum into a medium? State which attributes change and which stay the same and, thus, require the wavelength to decrease.

Does Huygens’s principle apply to all types of waves?

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