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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.

The figure shows two media separated by a horizontal line labeled surface. The upper medium is labeled medium one and the lower medium is labeled medium two. A vertical dotted line cuts through both media and is perpendicular to the surface. The point where the dotted line crosses the surface between the media will be called the point of contact. In medium one, a ray pointing down and to the right makes an abrupt turn at the point of contact. The path of the ray makes an angle theta sub one with the dotted line in medium one. In medium two, the ray leaves the point of contact and follows a path that makes an angle theta sub two with the dotted line in medium two, where theta sub two is less than theta sub one. We will call these the incident ray and the refracted ray, respectively. Thus, the refracted ray is closer to being vertical than the incident ray. Three line segments, labeled wavefront, are drawn perpendicular to the incident ray and the refracted ray. These line segments are equally spaced for both rays, but the three line segments that cross the incident ray are shorter and more widely spaced than the three line segments that cross the refracted ray. The separation of these line segments is labeled v sub one t for the incident ray and v sub two t for the refracted ray, with v sub two t being less than v sub one t.
Huygens’s principle applied to a straight wavefront traveling from one medium to another where its speed is less. The ray bends toward the perpendicular, since the wavelets have a lower speed in the second medium.

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, λ = c / f = ( 330 m / s ) / ( 1000 s 1 ) = 0 . 33 m size 12{λ=c/f= \( "330"`m/s \) / \( "1000"`s rSup { size 8{ - 1} } \) =0 "." "33"`m} {} , about three times smaller than the width of the doorway).

Part a of the figure is a view from above of a diagram of a wall in which is cut an open door. The wall extends from the bottom of the diagram to the top, and the door forms a gap in the wall. The door itself is opened to the left and is positioned about forty five degrees from the wall on which it pivots. From the left comes a bright light, which is labeled small lambda, and the door and wall create sharp shadows by blocking this light. The edges of these shadows are labeled straight-edge shadows. Some of the light passes through the open doorway. Part b of the figure shows a similar diagram. A line parallel to the wall approaches the wall from the left and is labeled plane wavefront of sound. There are five dots evenly spaced across the open doorway, labeled one through five. Semicircles appear to the right of these dots entering the room to the right of the wall. Bracketing all these semicircles is a line that has the form of closing square bracket with rounded corners. This line is labeled sound. There are five rays shown pointing from the bracketing line into the room to the right of the wall. Three of these rays point horizontally to the right, one ray points upward and to the right, and the last ray points downward and to the right. This last ray points to the ear of a person who we see from above and who is labeled listener. The diagram indicates that the listener hears sound around the corner of the door.
(a) Light passing through a doorway makes a sharp outline on the floor. Since light’s wavelength is very small compared with the size of the door, it acts like a ray. (b) Sound waves bend into all parts of the room, a wave effect, because their wavelength is similar to the size of the door.

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.

Three related diagrams showing how waves spread out when passing through various-size openings. The first diagram shows wavefronts passing through an opening that is wide compared to the distance between successive wavefronts. The wavefronts that emerge on the other side of the opening have minor bending along the edges. The second diagram shows wavefronts passing through a smaller opening. The waves experience more bending. The third diagram shows wavefronts passing through an opening that has a size similar to the spacing between wavefronts. These waves show significant bending.
Huygens’s principle applied to a straight wavefront striking an opening. The edges of the wavefront bend after passing through the opening, a process called diffraction. The amount of bending is more extreme for a small opening, consistent with the fact that wave characteristics are most noticeable for interactions with objects about the same size as the wavelength.

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)

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

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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?

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

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

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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.

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

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Questions & Answers

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Practice Key Terms 2

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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