Reflection, Refraction, and Diffraction

8/2/2019 Reflection, Refraction, and Diffraction

1/19

Refraction and DiffractionChapters 22 and 24


2/19

Electromagnetic Spectrum - Know

It!**At least the trend in wavelength and frequency


3/19

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)

=


4/19

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


5/19

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!


6/19

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 -


7/19

Dispersion Separation of white lightinto colored components

Shorter wavelengths diffract more than

longer ones


8/19

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


9/19

Critical Angle

Critical AngleAngle at which the refracted ray isparallel to the boundary


10/19

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)


11/19

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


12/19

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


13/19

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


14/19

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.)


15/19

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)


16/19

Polarization

Polarized wavesin same direction

Minimumtransmission when

at right angles;Maximum whenparallel

How sunglasseswork

Anothergreatillustration is in thebook (Figure 24.27)


17/19

Extra DiagramsDiagrams further defining toward the normal andaway from the normal in refraction


18/19

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


19/19

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

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Reflection, Refraction, and Diffraction