Download Chapter 22: Reflection and Refraction of Light

Chapter 22: Reflection and Refraction of Light
What is Light?
 Sir Isaac Newton first proposed that light was a tiny stream of
particles emitted by the light source.
 Thomas Young noticed that given light under certain conditions it
could cancel itself due to interference.
o Interference is a wave property!
 Einstein took it one step further to explain the photoelectric effect.
o Thus creating photons, or tiny particles of energy that are
transferred by a light wave.
 Because light has wave like and particle like properties, light is then
described by a wave-particle duality.
Electromagnetic Waves
 For much of our introductory purpose, we will only consider the
wave property of light.
 Since we can cancel out the wave property of light but still have
energy emitted, there must be more to the wave than just the light.
 This leads to light fitting being an electromagnetic wave.
o That is it contains perpendicular electric fields and magnetic
fields that oscillate perpendicular to the wave flow.
 So light waves travel as transverse waves.
Speed of Light
th
 Up until the 17 century, scientists believed there was no such thing as the “speed of light.”
o The belief was that light could travel any distance in no time at all.
 Galileo disagreed and tried to measure the speed of light by using lanterns one mile away from each other and
measuring the time it took for one assistant to see the lantern from the other assistant.
o Needless to say, that experiment yielding very little results.
 French physicist Hyppolite Fizeau developed one of the most accurate methods for measuring the speed of light.
o He sent a single beam of light through a rotating cogged wheel to a mirror
several kilometers away, and rotated the wheel at just the right speed that
the light would return through another window in the cogged wheel.
o By knowing the distance between the mirrors and the angular speed of
the cogged wheel, Fizeau was able to calculate the speed of light to be
313,000,000 .
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American physicist Albert Michelson expanded on Fizeau experiment from 1849
with better technology in 1877 to measure light more at the more commonly used
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measurement we have today of 2.99792458 x 10 .
o This measurement confirmed the work of Scotish physicist James Clerk Maxwell who had taken the
electromagnetic works of Faraday, Gauss, and Ampère and combined them into what are now called the
Maxwell Equations.
 All of which use the assumptions of vacuum permittivity ( ) and magnetic permeability ( ) from
the speed of light as it travels in a vacuum.
√
Because we consider the speed of light in a vacuum to be a constant standard, the letter c is used to replace v
when we discuss the speed of light in a vacuum.
o Notice, light does not need a medium to travel through but will travel through mediums of higher density
at a slower speed than it does in a vacuum.
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Ray Approximation of Light Waves
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To gain a better understanding of the behavior of light, we approximate the transverse wave
nature of the light travel to that of a single ray of light.
From experience, you may have noticed that light will travel in a straight line path until it
encounters a boundary between two different materials.
We approximate that straight line path with the use of rays to represent the direction of the light
travel.
o When using multiple rays are used, we agree that they all travel parallel to one another.
o While at the same time traveling perpendicular to the wavefronts of the actual light wave itself.
Intensity of Spherical Light Waves
 For our elementary understand we image a single light source such as a candle flame or a light bulb.
 The intensity of light refers to the perceived brightness of the light source.
o The farther one is from the source of light, the less bright the light appears to be.
 That is because the energy emitted by the light source spreads outward in all directions.
o Keep in mind, that the energy of each wavefront is equal to the
energy emitted from the light source.
 Recall, that intensity is defined as the rate of energy transferred through a
given area.
(
)

Due to light spreading out in all directions, the energy of each wavefront is
spread out over a spherical shell of travel. Thus
o
o
o

where P is the power of the light source measured in watts. (W)
r is the distance away from the light source measured in meters. (m)
and I is the intensity of the light source at that location measured in
watts per square meter. ( )
Notice, the intensity of light, much like the intensity of sound waves, follows the inverse-square law in which the
intensity diminishes as a result of the squared separation from the light source.
o Meaning: Moving twice as far away from the light source will result in an intensity level one-fourth the
original intensity.
Reflection
 Any time a light ray encounters the surface of a new medium, part of the light ray is reflected.
 In a mirror, some light is reflected upon entering the glass and the rest is reflected
when it hits the metallic backing.
 The new light rays will now travel parallel together, assuming the surfaces were
smooth.
 Reflection from a smooth surface is often called specular reflection.
o Specular reflection produces a discernible image that can be identified
 Reflection from a rough surface such as cloth or wood is often called diffuse
reflection.
 For our studies, we will assume all reflection is specular in nature unless told
otherwise.
The Law of Reflection
 From observation, the angle of reflection is equal to the angle of incidence.
o Incidence indicates the original path of entry.
 However, the angle is measured from a line perpendicular to the surface that we call the normal.
 We use the perpendicular line because using the mirror itself could vary based on the shape and surface quality
of the mirror at the incidence point.
 The angle is of incidence is represented by the variable 1.
o Some texts use i.
 The angle of reflection uses the variable 1’.
o Some texts use r.
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Red Eye
 Red eye is often seen in photographs taken with a flash.
 This shows an example of retroreflection.
 Retroreflection is reflection that travels back along its original direction.
o So what you are seeing is the light reflecting off the blood vessels in the retina
of your eye and returning back out the lens of the eye.
Refraction
 All electromagnetic waves, light included, travel at the same speed while they remain in the same medium.
o With electromagnetic waves traveling the fastest in a vacuum.
 However, when a light ray encounters a new medium, it will not travel as fast in the new medium because:
o Using the photon characteristic of light, the energy carried by the massive photon may be absorbed by
atoms of the medium and released a short time later or it may collide with other atoms giving it a longer
path and thus a longer amount of time to travel through the medium.
 Keep in mind the photon itself is still traveling at the speed of light in a vacuum. (
)
o Using the wave characteristic of light, just like surface waves in a lake that near the
shore, the bottom part of the wave may slow down before the top and thus the waves
crashes over.
 In the case of a light wave, one part of the wave from enters the medium and
slows down before the rest of the wave front and this causes the overall
direction of the wave front to bend inward towards the normal line.
 Do not forget, when any wave, electromagnetic waves included, encounter a new medium of a
different density medium, part of the ray is reflected at the boundary and the rest enters the medium and is bent.
 This bending, or altering, of the original wave path is called refraction.
Angle of Refraction
 The angle of refraction, 2, is again measured with respect to a normal line drawn with the
boundary and it depends on
o the speed of light as it travels in the medium
 which is determined essentially by the optical “density” of the medium, and
o the incoming angle of incidence
 Remember, the light is bent because one side of the wave will travel slower in a more “optically dense” medium.
o So when light travels from a vacuum (where it travels the fastest it can) into glass, the wave will be bent
towards the normal.
o The reverse is also true, when light travels from glass to a vacuum it will bend away from the normal.
Snell’s Law
 Willebrord Snell (1591 –1626) is credited with the discovery of how light behaves when it changes medium.
 He saw a relationship between the angle of incidence and the speed of light
traveling through that medium.
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
o
o
o
o
with 1 being the angle of incidence
and 2 being the angle of refraction
while v1 is the speed of light in the incident medium. (before the surface)
and v2 is the speed of light in the refracting medium. (after the surface)
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both velocities should be measured in the same units, preferably meters per second. ( )
Referring to the unit circle, the sin  increases in magnitude as  increases from 0 to 90.
Again, that reinforces that when light travels from a vacuum to another medium, the angle must get closer to 0.
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Law of Refraction
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When light passes from one transparent medium to another, it is refracted because the speed of light is different
in the two media.
As light travels from one medium to another, its frequency does not change.
o Think about connect a light string to a heavy string. When the light string is sent into a transverse wave
pattern, the heavy string is connected to it and vibrates up and down every time the light string does. That
vibrating up and down rate is the frequency.
)
So if frequency stays the same, then wavelength and speed are the variables that can change. (
Index of Refraction
 In the early 1800’s several physicists and mathematicians, including Thomas
Young and Charles Hutton, set out to create a scale of comparison speeds of the
speed of light in varying substances.
o This was done in an effort to explain the changing angle as observed by
Snell without having to measure the speed of light directly.
 Which seems like an admirable task considering the how fast
the speed of light is known to be.
 What was established was what we call the index of refraction.
 This is a ratio of the speed of light in a refractive medium compared with the
speed of light in a vacuum.
with c being the speed of light in a vacuum. (
)
while v is the speed of the light in the refracting medium also measured
in meters per second.
o and n is the unitless index of refraction.
Since we use the speed of light in a vacuum as our baseline, the lowest index of
refraction exists in a vacuum as n = 1.000.
Any other refractive medium will have an index larger than 1.
o By definition, the index of refraction will indicate how much faster light travels in a vacuum than in the
refracting medium.
 For instance, the index of refraction for water is n = 1.333. So light travels 1.333 times faster in a
vacuum than it does in water.
Keep in mind, the index of refraction can varying for most mediums based on the wavelength of the light and the
temperature of the two respective mediums.
o We will revisit this phenomenon later with our discussion of prisms and dispersion. Until then, assume the
index of refraction is based on uniform wavelengths and temperatures for all problems.
o
o
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Snell’s Law Revised
 Remember, Snell made his observations in 1621 well before Young and Hutton in the early 1800’s introduced the
idea of an index of refraction.
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Using the defined ratio of the index of refraction, substitute into Snell’s initial relationship for v.
(
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)
o
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That way the unknown speeds of light in the refracting mediums can be replaced by the now constant
value for the speed of light.
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By doing a little cross-multiplying and cancelling of the constant speed of light, c. (
)
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Rearrange so like terms are on like sides of the equation, producing the more common form of Snell’s Law:

o
o
o
o
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
where n1 is the index of refraction for the incident medium. (before the surface)
with 1 being the angle of incidence
and n2 is the index of refraction for the refracting medium. (after the surface)
and 2 being the angle of refraction
 Sometimes it is convenient to think of the subscript “1” as the initial medium of the light travel and
subscript “2” as the final medium of light travel.
This equation can be used with any two refracting mediums, neither of which need to be a vacuum.
o So with that said, you may want to just remember that the index of refraction for a vacuum is n = 1.000
o Any other index of refraction will either be the unknown variable, or it will be given to you in the problem.
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Light Spectra
 Up until now we have treated all incoming light to a boundary as white light all traveling with the same wavelength
and frequency, and that is technically not true.
 The visible light spectrum consists of seven colors that all mix to make white light. (ROY G. BIV)
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When referencing one color, or hue, that is called monochromatic light.
So as a general rule for the seven monochromatic hues of the visible spectrum:
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o Red light has the largest wavelength (625 – 780 nm ) with the smallest frequency (380 – 460 x 10 Hz)
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o Violet light has the smallest wavelength (380 – 430 nm) with the largest frequency (700 – 790 x 10 Hz)
Dispersion
 The index of refraction for each material actually varies based on the wavelength.
 Remember, refraction occurs because the speed of the wave, or any part of the wave in the
new medium changes while the frequency of the wave does not. So that must mean the
)
wavelength will change to tie in with the speed change. (
 For monochromatic light, a larger wavelength will have a smaller index of refraction.
 So when white light is incident on the surface of a refracting medium, red light will bend less than violet
light.
 Essentially, the red waves of the white light will not slow down less the violet waves, so red will bend less.
 That is why red is on top of the rainbow! It doesn’t
bend as much as the others.
 This separating white light into its individual monochromatic
hues by using refraction is called dispersion.
 Prisms are a common device to exaggerate the effects of
dispersion because the colors that bend more also have to
travel through more of the refracting medium of the colors that
do not refract as much.
Atmospheric Refraction
 As light from the Sun travels through space, it is traveling in a vacuum. So when that light enters our atmosphere,
it will slow down slightly.
 When the light enters perpendicular to our atmosphere, it will not be bent and
each wavefront will slow down uniformly.
 However, when the light enters our atmosphere at an angle, then refraction will
occur.
 This refraction is most prominent at sunrise and again at sunset.
o When you think of the different layers of our atmosphere, you will see
that the light from the Sun will be refracted numerous times.
o With that said, when we see the sunrise in the morning our eyes are
fixed at an angle of where we see the sun enter the atmosphere after refraction.
 But really the Sun is still below the horizon.
 Therefore, without atmospheric refraction the sunrise would be later in the day and sunset would be sooner
o Because we again see the sun after refraction that allowed it to bend more towards the Earth after it fell
below the horizon; which at the time of sunset or sunrise is our normal line!
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Internal Reflection
 Up until now, we have primarily discussed the behavior of light when it travels from a medium of low index of
refraction (high velocity) into a medium of high index of refraction (low velocity).
 If you remember, when light travels into a medium in which is will slow down, the path of the light will be bent
toward the normal.
 So what will happen to light when it travels into a medium in which it will speed up?
 Actually, one of two things may occur:
1. Part of the ray will be reflected and the rest will refract and bend away from
the normal.
2. The incident ray will undergo total internal reflection.
Critical Angle
 Using the wave property of light along with Snell’s Law can explain why internal reflection may occur.
 As Snell observed, light will bend away from the normal (closer to the boundary surface).
o That is because now, part of the wavefront has been able to speed up while the remaining portion in the
more optically “dense” medium is traveling slower.
 If the difference in optical “densities” is large enough, or the angle is shallow enough (large as measured from the
normal), the portion of the wave front that sped up is able to completely turn around before the rest of the wave
exits the medium of higher index of refraction.
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It is not a sure thing when going from a higher index of refraction to a lower index of refraction to have total
internal reflection occur.
That cutoff for when it will occur is called the critical angle. ( )
o At angles larger than the critical angle, total internal reflection will occur.
 Remember, the angle is measured with the perpendicular normal.
o At angles smaller than the critical angle, partial internal reflection will occur
with refraction as most of the light ray will exit the medium.
o When the incident ray is measured to be at the critical angle, the resulting
ray will travel along the surface of the medium.
 This may illuminate the surface and simply exit the medium parallel
to the surface when the medium ends.
Calculating Critical Angle
 The critical angle will produce the critical ray, which travels along the boundary edge of the refracting medium.
 That means, that the angle of refraction for the critical ray is 90° from the normal.
(
)
 Snell’s Law works for all angles of refraction, even 90°.

 NOTICE: TOTAL INTERNAL REFLECTION CAN ONLY OCCUR WHEN TRAVELING FROM A MEDIUM OF
HIGHER INDEX OF REFRACTION INTO A MEDIUM WITH A LOWER INDEX OF REFRACTION.
 So for instance, the light is traveling in glass now and is passing out into a vacuum.
 Thus, when calculating the critical angle, n1 is now the index of refraction for the refracting device such as the
glass, or water, or Lucite, etc.
 In solving Snell’s Law for a 90 angle of refraction, we find a relationship used for calculating the critical angle:

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where n2 is the index of refraction for the outside layer
and n1 is the index of refraction for the inside layer
while c is the critical angle (which in Snell’s Law was the angle of incidence, or 1)
 By understanding the design of the sine ratio, you must realize
 That also reinforces the observation of when total internal reflection can occur.
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Fiber Optics
 Fiber optic cables use internal reflection to send light, or any electromagnetic wave for that matter, over long
distances for the purpose of data and information gathering and measuring.
 A fiber optic cable consists of a transparent core surrounded by refractive cladding of lower index of refraction
than the core.
 That cladding then gives the cable the ability to turn corners while still maintaining the refractive
relationship necessary to provide total internal reflection throughout the entire fiber.
 Fiber optic cables are better than using electrical pulses because the cables are less likely to build up heat and
heat creates unwanted resistance in electrical circuits.
Color
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The color of an object is dependent on the reflecting and absorbing properties of the material.
The color we see is the reflected light from the material.
So if all the light is reflected off the surface, then the color we see is the color that was transmitted to the material.
Some light may be absorbed in the form of heat and some transmitted through the material.
o Remember, every time a wave hits a boundary, some of the wave is reflected and most is transmitted.
Primary Colors v Additive Colors of Light
 Elementary colors are those colors that are split from the rainbow.
o Red, orange, yellow, green, blue, indigo & violet.
 Three of those colors cannot be formed from any other two.
o Red, Yellow, & Blue
 Since white light can be split into elementary colors, it is safe to assume that elementary
colors can be mixed to form other colors.
 Due to the interference and intensity properties of light, yellow and green behave differently
than pigments.
o Yellow can actually be created from red and green.
o However, green cannot be formed from anything else.
 So the primary additive colors of light are:
o Red, Green, & Blue
 We call them additive colors because as they are mixed together they form a new color.
 The primary pigments are referred to as subtractive colors of light.
o That is because the pigment that we see is really that color of light it intends to give off.
o The other colors are absorbed, or subtracted from white light.
 For instance, yellow pigment is intended to reflect a mix of red and green light only. So blue light is subtracted.
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