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8/2/2019 Reflection, Refraction, and Diffraction
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Refraction and DiffractionChapters 22 and 24
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Electromagnetic Spectrum - Know
It!**At least the trend in wavelength and frequency
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Law of Reflection
Angle of incidence ()Angle at which the ray hitsthe boundary
Angle of Reflection ()
Angle at which the reflectedray leaves the boundary
Angle of Incidence =Angle of Reflection
NOTE: Angle is measuredfrom the normal(perpendicular to boundary;dotted line in diagram)
=
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Refraction
Bending of waves entering a new (different) medium
Angle of incidence () Angle at which the ray hits theboundary
Angle of Refraction () Angle at which the ray moves throughthe new medium
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RefractionIf velocity in newmedium is less thanvelocity in oldmedium, the wavesbend toward thenormal (Second
Diagram)
If velocity in newmedium is morethan velocity in oldmedium, the waves
bend away from thenormal (FirstDiagram)
NOTE: Only speed and wavelength changein refraction. Frequency stays the same!
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Index of Refraction
Ratio of the speed of the wave in a vacuum to the speed of thewave in the medium
n must be greater than or equal to 1 (See Proof 1)
Snell's Law -
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Dispersion Separation of white lightinto colored components
Shorter wavelengths diffract more than
longer ones
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More on Reflection and Refraction
Incident rays areusually both reflectedand refracted
If index of refraction of
other medium is greatthan index of currentmedium, a 180 phasechange occurs inreflection (troughbecomes crest and vise
versa)
Otherwise, there is nophase change
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Critical Angle
Critical AngleAngle at which the refracted ray isparallel to the boundary
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Total Internal Reflection Total Internal Reflection Occurs when the incoming rayis completely reflected back into the medium from whencethe ray originated (Diagram 2)
Total Internal Reflection can only occur in changing from ahigher index of refraction to a lower one (See Proof 2)
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Conditions for Interference Source of wave must
be coherent
Coherent Lightallwaves must be of thesame wavelength andmust be in phase with
respect to the others
Example ofCoherent LightLaser (bottom picture)
Example ofIncoherent LightRegular or FilteredLight (first 2 pictures
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Thin Film Interference Recall when waves reflect off a low index-high index boundary, a
180 phase shift occurs, but the refracted ray does not undergoa phase change
The refracted ray reflects off the bottom surface (with or withouta phase change depends on index of other medium at
boundary), and once again refracts through the top boundary In order to obtain constructive interference, the two rays exiting
the film (one reflected off, one refracted from) must be in phase
Therefore, the distance the wave travels in the film must be halfa wavelength in order to get it back in phase with the initial
reflected ray
NOTE: Remember that the initial refracted ray travels throughthe film in two directions, so the half wavelength is equally splitbetween the two paths
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Thin Film Interference, cont. This results in the thickness of the film being equal
to an odd-fourth multiples (if there are an odd numberof phase changes; , , etc.) or even-fourthmultiples (if there are an even number of phasechanges; 2/4, 4/4, etc. ) of the wavelength
Real-lifeExamples:
Bubbles, Oilon pavement
2t = m
t = thicknessof film
m = numberof wavelengthsinside film
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Diffraction Constructive Interference (Maxima) represented by bright
bands
Destructive Interference (Minima) represented by darkbands
Order of Maxima/Minima (represented by m) number of
bands away from center (Zero order)
Order counts in either direction (1st order maximum to theright or to the left (and so on...)
Minima have half-orders(m = .5, 1.5, 2.5, etc.)
Maxima have wholenumber orders (m = 0, 1, 2,etc.)
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Single Slit Diffraction
x = distance to maximum orminimum
L = distance to screen from slit
d = width of slit*
m = order of maximum orminimum (can be any order,though 1st is generally used)
= angle formed by x and L
x/L can be substituted for sin at small angles because sin =tan
* Watch out! Often they willgive you the number of linesper unit distance. You want thereciprocal (distance/line)
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Polarization
Polarized wavesin same direction
Minimumtransmission when
at right angles;Maximum whenparallel
How sunglasseswork
Anothergreatillustration is in thebook (Figure 24.27)
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Extra DiagramsDiagrams further defining toward the normal andaway from the normal in refraction
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Proof 1
Prove: Index of refraction (n) 1
Required Equation(s)/Concepts: n = c/v
v cannot be greater than c (the speed of light in a vacuum), so atmost, v can equal c
If v = c, n = c/c, or n = 1
If v < c, the denominator is smaller than the numerator;therefore, n > 1
Conclusion: n 1
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Proof 2
Prove: Total Internal Reflection can only occur in changing froma higher index of refraction to a lower one
Required Equation(s)/Concepts: -1 sin t 1; Critical AngleFormula
Sin t cannot be greater than 1
n2/n1 must therefore be less than or equal to 1
If n1 < n2, then sin t > 1, which is impossible
Conclusion: In order for sin t 1 to remain true, n1 must be n2