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Check Your Understanding [link] shows that ethanol and fresh water have very similar indices of refraction. By what percentage do the speeds of light in these liquids differ?

2.1% (to two significant figures)

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The ray model of light

You have already studied some of the wave characteristics of light in the previous chapter on Electromagnetic Waves . In this chapter, we start mainly with the ray characteristics. There are three ways in which light can travel from a source to another location ( [link] ). It can come directly from the source through empty space, such as from the Sun to Earth. Or light can travel through various media, such as air and glass, to the observer. Light can also arrive after being reflected, such as by a mirror. In all of these cases, we can model the path of light as a straight line called a ray    .

The figure has drawings illustrating the three methods for light to travel from a source to another location. Figure a shows light from the sun reaching the earth’s atmosphere, traveling in a straight line through space. Figure b shown light traveling through a window to reach an observer. Figure c shows light traveling from an object to a mirror and reflecting toward the observer.
Three methods for light to travel from a source to another location. (a) Light reaches the upper atmosphere of Earth, traveling through empty space directly from the source. (b) Light can reach a person by traveling through media like air and glass. (c) Light can also reflect from an object like a mirror. In the situations shown here, light interacts with objects large enough that it travels in straight lines, like a ray.

Experiments show that when light interacts with an object several times larger than its wavelength, it travels in straight lines and acts like a ray. Its wave characteristics are not pronounced in such situations. Since the wavelength of visible light is less than a micron (a thousandth of a millimeter), it acts like a ray in the many common situations in which it encounters objects larger than a micron. For example, when visible light encounters anything large enough that we can observe it with unaided eyes, such as a coin, it acts like a ray, with generally negligible wave characteristics.

In all of these cases, we can model the path of light as straight lines. Light may change direction when it encounters objects (such as a mirror) or in passing from one material to another (such as in passing from air to glass), but it then continues in a straight line or as a ray. The word “ray” comes from mathematics and here means a straight line that originates at some point. It is acceptable to visualize light rays as laser rays. The ray model of light describes the path of light as straight lines.

Since light moves in straight lines, changing directions when it interacts with materials, its path is described by geometry and simple trigonometry. This part of optics, where the ray aspect of light dominates, is therefore called geometric optics    . Two laws govern how light changes direction when it interacts with matter. These are the law of reflection , for situations in which light bounces off matter, and the law of refraction , for situations in which light passes through matter. We will examine more about each of these laws in upcoming sections of this chapter.

Summary

  • The speed of light in a vacuum is c = 2.99792458 × 10 8 m/s 3.00 × 10 8 m/s .
  • The index of refraction of a material is n = c / v , where v is the speed of light in a material and c is the speed of light in a vacuum.
  • The ray model of light describes the path of light as straight lines. The part of optics dealing with the ray aspect of light is called geometric optics.
  • Light can travel in three ways from a source to another location: (1) directly from the source through empty space; (2) through various media; and (3) after being reflected from a mirror.

Conceptual questions

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

model as a ray when devices are large compared to wavelength, as a wave when devices are comparable or small compared to wavelength

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Why is the index of refraction always greater than or equal to 1?

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Does the fact that the light flash from lightning reaches you before its sound prove that the speed of light is extremely large or simply that it is greater than the speed of sound? Discuss how you could use this effect to get an estimate of the speed of light.

This fact simply proves that the speed of light is greater than that of sound. If one knows the distance to the location of the lightning and the speed of sound, one could, in principle, determine the speed of light from the data. In practice, because the speed of light is so great, the data would have to be known to impractically high precision.

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Speculate as to what physical process might be responsible for light traveling more slowly in a medium than in a vacuum.

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Problems

What is the speed of light in water? In glycerine?

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What is the speed of light in air? In crown glass?

2.99705 × 10 8 m/s ; 1.97 × 10 8 m/s

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Calculate the index of refraction for a medium in which the speed of light is 2.012 × 10 8 m/s , and identify the most likely substance based on [link] .

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In what substance in [link] is the speed of light 2.290 × 10 8 m/s?

ice at 0 ° C

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There was a major collision of an asteroid with the Moon in medieval times. It was described by monks at Canterbury Cathedral in England as a red glow on and around the Moon. How long after the asteroid hit the Moon, which is 3.84 × 10 5 km away, would the light first arrive on Earth?

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Components of some computers communicate with each other through optical fibers having an index of refraction n = 1.55 . What time in nanoseconds is required for a signal to travel 0.200 m through such a fiber?

1.03 ns

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Compare the time it takes for light to travel 1000 m on the surface of Earth and in outer space.

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How far does light travel underwater during a time interval of 1.50 × 10 −6 s ?

337 m

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Practice Key Terms 3

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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