Chapter 22
Reflection and Refraction
of
Light
Law of reflection and refraction
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The incident ray, the
normal and the
reflected ray are
coplanar.
θ 1 = θ1 ’
n1 sin θ1 = n2 sin θ2
Dispersion
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The index of refraction in anything
except a vacuum depends on the
wavelength of the light
This dependence of n on λ is called
dispersion
Snell’s Law indicates that the angle of
refraction made when light enters a
material depends on the wavelength of
the light
Variation of Index of
Refraction with Wavelength
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The index of refraction
for a material usually
decreases with
increasing wavelength
Violet light refracts
more than red light
when passing from air
into a material
Refraction in a Prism
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The amount the ray
is bent away from
its original direction
is called the angle of
deviation, δ
Since all the colors
have different
angles of deviation,
they will spread out
into a spectrum
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Violet deviates the
most
Red deviates the
least
Prism Spectrometer
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A prism spectrometer uses a prism to cause
the wavelengths to separate
The instrument is commonly used to study
wavelengths emitted by a light source
Using Spectra to Identify
Gases
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All hot, low pressure gases emit their
own characteristic spectra
The particular wavelengths emitted by a
gas serve as “fingerprints” of that gas
Some uses of spectral analysis

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Identification of molecules
Identification of elements in distant stars
Identification of minerals
The Rainbow
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A ray of light strikes a drop of
water in the atmosphere
It undergoes both reflection and
refraction
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First refraction at the front of the
drop
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Violet light will deviate the most
Red light will deviate the least
The Rainbow, 2
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At the back surface the
light is reflected
It is refracted again as
it returns to the front
surface and moves into
the air
The rays leave the drop
at various angles
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The angle between the
white light and the violet
ray is 40°
The angle between the
white light and the red
ray is 42°
Observing the Rainbow
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If a raindrop high in
the sky is observed,
the red ray is seen
A drop lower in the sky
would direct violet light
to the observer
The other colors of the
spectra lie in between
the red and the violet
Sunlight consists of all visible colors and water
Rainbows is dispersive, so when sunlight is refracted as it
enters water droplets, is reflected off the back
surface, and again is refracted as it exits the
water drops, the range of angles for the exiting
ray will depend on the color of the ray. Since
blue is refracted more strongly than red, only
droplets that are closer the the rainbow center
(A) will refract/reflect blue light to the observer
(O). Droplets at larger angles will still
refract/reflect red light to the observer.
What happens for rays that reflect twice off the
back surfaces of the droplets?
Fig. 33-22
3312
Total Internal Reflection
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Total internal
reflection can occur
when light attempts
to move from a
medium with a high
index of refraction to
one with a lower
index of refraction
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Ray 5 shows internal
reflection
Critical Angle
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A particular angle
of incidence will
result in an angle
of refraction of
90°

This angle of
incidence is called
the critical angle
n2
sin  C 
for n1  n2
n1
Critical Angle, cont
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For angles of incidence greater than the
critical angle, the beam is entirely
reflected at the boundary
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This ray obeys the Law of Reflection at the
boundary
Total internal reflection occurs only
when light attempts to move from a
medium of higher index of refraction to
a medium of lower index of refraction
Fiber Optics
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An application of
internal reflection
Plastic or glass rods
are used to “pipe”
light from one place
to another
Applications include
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Medical use of fiber
optic cables for
diagnosis and
correction of medical
problems
Telecommunications
R > nd/(n-1)
Solution 22.52
(a) A ray originally traveling along the inner edge will
have the smallest angle of incidence when it strikes the
outer edge of the fiber in the curve. Thus, if this ray is
totally internally refl ected,
all of the others are also totally reflected. For this ray to
be totally internally reflected it is necessary that θ≥θc or
sinθ≥sinθc = 1/
But, sinθ = (R-d)/R, so we must have (R –d)/R ≥ 1/n
which simplifies to R ≥ nd /(n−1)
(b) As d→0, R→0. This is reasonable behavior.
As n increases, Rmin = nd/(n-1) = d/(1-1/n) decreases.
This is reasonable behavior.
As n→1, Rmin increases. This is reasonable behavior.
(c) Rmin = nd/(n-1) = 1.4x100μm/(1.4-1) = 350 μm
22.20
What is the index of refraction?
22.20
Since the light ray strikes the first surface at normal
incidence, it passes into the prism without deviation.
Thus, the angle of incidence at the second surface
(hypotenuse of the triangular prism) is θ1=45.0°, as
shown in the sketch at the right. The angle of refraction
is θ2 =45.0°+15.0°=60.0° and Snell’s law gives the
index of refraction of the prism material as
n2 = n1 sinθ1/ sin θ2
= 1 sin 60/sin 45 = 1.22
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20.49
What is θ4 ?
n2 is increased, at what
value of n2 the light beam
goes straight through?
20.49 solution
θ1 = 60 = θ2
θ3 +90 +30+30 = 180 => θ3 = 30
n1 sin 30 = sinθ4
θ4 = 38.5
 n2 > n1 sin 60 = (1.66) sin60 = 1.44
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