Vern J. Ostdiek Donald J. Bord Chapter 9 Optics (Section 3)

Vern J. OstdiekDonald J. Bord

Chapter 9Optics

(Section 3)

9.3 Refraction

• Imagine a light ray from some source in air arriving at the surface of a second transparent substance like glass. • The boundary between the air and glass is called

the interface. • Some of the incident light is reflected back into the

air, but the rest of it is transmitted across the interface into the glass.

• The law of reflection gives us the direction of the reflected light ray, but what about the transmitted light ray?

9.3 Refraction

• The light that passes into the glass is refracted—the transmitted ray is bent into a different direction than the incident ray. • Only if the incident ray is perpendicular to the

interface is there no bending.

• This bending is caused by the fact that light travels slower in glass than in air.

9.3 Refraction

• We again draw in the normal, a line perpendicular to the interface. • The angle between the transmitted ray and the

normal, called the angle of refraction, is smaller than the angle of incidence.

9.3 Refraction

• We can also have the reverse process: • A light ray traveling in glass

reaches the interface and is transmitted into air.

• In this case, the angle of refraction is larger than the angle of incidence.

9.3 Refraction

Law of Refraction: A light ray is bent toward the normal when it enters a transparent medium in which light travels more slowly. • It is bent away from the normal when it enters a

medium in which light travels faster.

9.3 Refraction

• Notice the symmetry in the figures.• This is one example of the principle of reversibility:

• The path of a light ray that is refracted at an interface is reversible.

9.3 Refraction

• The path that a ray takes when going from air into glass is the same path it would take if it turned completely around and went from glass into air. • In all of the figures in this and the following

sections, the arrows on the light rays could be reversed and the paths would be the same.

9.3 Refraction

• Refraction of light affects how you see things that are in a different medium, such as under water. • The figure on the left shows a coin at the bottom of

an empty glass; • On the right is the same coin at the bottom of a

glass full of water.

9.3 Refraction

• Note the difference in the sizes of the coin in the two photos. • The coin in the figure on the right appears larger

because the image of the coin formed in water is closer to the observer than the image formed in air.

9.3 Refraction

• The figure displays a ray diagram for this circumstance revealing how the bending of the rays of light from the edges of the coin as they enter the air from the water causes the coin to appear to be closer to the surface than it is.

9.3 Refraction

• The speed of light in any transparent material is less than the speed of light c in a vacuum. • For example:

c = 3×108 m/s in vacuum

the speed of light in water = 2.25×108 m/s

the speed of light in diamond = 1.24×108 m/s

9.3 Refraction

• The table gives the speed of yellow light in selected transparent media.

9.3 Refraction

• At this point, you may have two questions in mind.• Why is the speed of light lower in transparent media

such as water and glass, and • why does this cause refraction?

• To answer the first question, we must remember that light is an electromagnetic wave—a traveling combination of oscillating electric and magnetic fields. • As light enters glass, the oscillating electric field of

the wave causes electrons in the atoms of the glass to oscillate at the same frequency.

9.3 Refraction

• These oscillating electrons emit secondary EM waves (light) that travel outward to neighboring electrons.

• However, the wave emitted by each electron is not exactly “in step” with the primary incident wave that is causing the electron to oscillate: • The secondary wave lags the primary wave slightly.

• This means, for example, that a secondary wave crest arrives at a given point in the medium a little bit later in time than the corresponding primary wave crest.

9.3 Refraction

• As the process repeats from electron to electron, these phase lags accumulate, yielding a net EM disturbance formed from the addition of the primary and secondary waves whose speed of propagation through the medium is reduced.

9.3 Refraction

• As to the second question, we can see why a change in the speed of light causes bending by carefully following wavefronts as they cross an interface.

9.3 Refraction

• A good analogy to this is a marching band, lined up in rows, crossing (at an angle) the boundary between dry ground and a muddy area.

9.3 Refraction

• Each person in the band is slowed as his or her feet slip and sink in the mud. • To remain aligned and properly spaced, each

person has to turn a bit, and the whole band ends up marching in a slightly different direction.

9.3 Refraction

• A similar change in direction occurs for light entering glass. • Adding together the slower moving wavefronts

emitted by the electron oscillators located at different distances from the interface in a way that respects their relative phases produces a net (total) wavefront that propagates in a different direction compared to that of the incident wave.

• Note that the reduction in speed also makes the wavelength shorter.

9.3 Refraction

• This has to be the case because the frequency of the wave remains the same and we must have:

v = f • The law of refraction was discovered in 1621 by the

Dutch physicist Willebrord Snel and later expressed in its common form by the French mathematician René Descartes.

• It gives the exact value of the angle of refraction when the angle of incidence and the speeds of light in the two media are known.

9.3 Refraction

• The graph in the figure shows the relationship between the two angles for an air-glass boundary. • A similar graph could be constructed for other

different pairs of media.

9.3 Refraction

• The angle between the normal and the light ray in air is plotted on the horizontal axis, and the corresponding angle for the ray in glass is plotted on the vertical axis. • Notice that the angle in glass is smaller than the

angle in air.

9.3 Refraction

• For a ray going from air into the glass, this means that the angle of refraction is smaller than the angle of incidence. • For the largest possible angle of incidence, 90, the

angle of refraction is about 43.

9.3 RefractionExample 9.1

• The figure depicts a light ray going from air into glass with an angle of incidence of 60. • Find the angle of refraction:


• We use the graph with the angle in air equal to 60.• Locate 60 on the horizontal axis, follow the dashed

line up to the curve, and then move horizontally to the left.


• The point on the vertical scale indicates the angle in glass is about 36. • Therefore, the angle of refraction is 36.

9.3 Refraction

• But what happens to light that passes completely through a sheet of glass like a windowpane? • Each light ray is bent toward the normal when it

enters the glass and then is bent away from the normal when it reenters the air on the other side.

• No matter what the original angle of incidence is, the two bends exactly offset each other, and the ray emerges from the glass traveling parallel to its original path.

9.3 Total Internal Reflection

• Consider now the following experiment shown schematically in the figure.• Rays of light

originating in glass strike the boundary (separating it from the surrounding air) at ever-increasing angles.


• In this case, because the speed of light in glass is smaller than the speed of light in air, we see that the ray is bent away from the normal. • In other words, the angle of refraction is larger than

the angle of incidence, as shown the figure. • Moreover, the angle of refraction increases as the

angle of incidence does.


• Because of reversibility we can use the same graph to find the angle of refraction when the angle of incidence is known. • In this situation, the angle of incidence is the “angle

in glass,” whereas the angle of refraction is the “angle in air.”


• For example, when the angle of incidence is 20, we locate 20 on the vertical scale, move horizontally to the curve, and then drop down to the axis where we see that the angle of refraction would be about 30.


• What distinguishes this case from the previous one, in which the incident ray was in air, is the existence of a critical angle of incidence for which the angle of refraction reaches 90. • When the angle of incidence equals this critical

angle, the transmitted ray travels out along the interface between the two media.


• For angles of incidence greater than the critical angle, the formerly transmitted ray is bent back into the incident medium and does not travel appreciably into the second medium.• When this happens, we have a condition called

total internal reflection.


• In general, different media have different critical angles. • The table includes the values of the critical angle

for light rays entering air from different transparent media.


• Notice that the critical angle is smaller for materials in which the speed of light is lower. • Diamond, with the lowest speed of light in the list,

has a critical angle of less than 25—little more than half that of glass.

9.3 Total Internal Reflection Example 9.2

• A homeowner wishes to mount a floodlight on a wall of a swimming pool under water so as to provide the maximum illumination of the surface of the pool for use at night. • At what angle with respect to the wall should the

light be pointed?

9.3 Total Internal Reflection Example 9.2

• To illuminate the surface of the water, the refracted ray at the water-air interface should just skim the water’s surface. • This means that the angle of refraction must be 90,

so the incident angle must be the critical angle. • The critical angle for water is about 49.

• The homeowner should direct the floodlight upward so that the beam makes an angle of roughly 49 with the vertical side wall of the pool.


• Optical fibers are flexible, coated strands of glass that utilize total internal reflection to channel light. In a sense, an optical fiber does to light what a garden hose does to water.• The figure shows the path of a particular light ray as

it enters one end of an optical fiber.• When this ray strikes the wall of the fiber, it does so

with an angle of incidence that is greater than the critical angle, so the ray undergoes total internal reflection.


• This is repeated each time the ray encounters the fiber’s wall, so the light is trapped inside until it emerges from the other end. • You may have seen decorative lamps with light

bursting from the ends of a “bouquet” of optical fibers.

• Fiber-optic cables consisting of dozens or even hundreds of individual optical fibers are now in common use to transmit information.


• Telephone conversations, audio and video signals, and computer information are encoded (“digitized”) and then sent through fiber-optic cables as pulses of light produced by tiny lasers. • A typical fiber-optic cable can transmit thousands of

times more information than a conventional wire cable that is much larger in diameter.


• For example, the first fiber-optic transatlantic cable, which went into service in 1988, was designed to carry 40,000 simultaneous conversations over just two pairs of glass fibers. • By contrast, the last of the large copper bundles

installed for overseas communications (1983) could handle only about 8000 calls.


• One significant advantage of using optical fibers to conduct light from one place to another is their flexibility. • If bundles of free fibers are bound together in a way

that preserves the relative positions of adjacent fibers from one end to the other, the bundle may transmit images as well as light.


• Devices incorporating this technology are routinely used to examine hard-to-reach places like the insides of a nuclear reactor, a jet engine, or the human body.• When used in the latter capacity, the instrument is

generally called an endoscope. • Specific examples of endoscopes include

bronchoscopes (for examining lung tissue), gastroenteroscopes (for checking the stomach and digestive tract), and colonoscopes (for surveying the bowel).

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Vern J. Ostdiek Donald J. Bord Chapter 9 Optics (Section 3)