today5/1 questions? waves (review) phase shifts interference reftaction lenses/mirrors etc
Post on 25-Dec-2015
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Interference in 2-DSources “in phase”
Crest meets crest and trough meets trough, constructive, loud sound or bright light
Crest meets trough and trough meets crest, destructive, no sound or dark
Crest
Trough
Interference in 2-DSources “in phase”
Constructive at a point if it is the same distance from each source
Destructive at a point if it is 1/2 farther away from one source
Crest
Trough
Interference in 2DSources “out of phase”
Crest meets trough and trough meets crest, destructive, no sound or dark
Crest meets crest and trough meets trough, constructive, loud sound or bright
Crest
Trough
Interference in 2-DSources “out of phase”
Destructive at a point if the point is the same distance from each source
Constructive at a point if the point is 1/2 farther away from one source
Crest
Trough
Fixed End Reflections
Fixed end
Crest turns into trough
Leading edge is the same
See “Wave Interference” handout for how the string looks during the reflection.
Same velocity, length, and amplitude
Free End Reflections
Free end
Crest stays a crest
Leading edge is the same
See “Wave Interference” handout for how the string looks during the reflection.
Same velocity, length, and amplitude
Light to HeavyBoth transmission and reflection
Boundary feels like a fixed end to the light string
Reflection just like fixed end, inverted
Transmitted wavelength has the same shape except it’s shorter in length because it travels slower than the incoming wave.
Slower, so not as far from boundary
Shorter, “bunched up” Inverted wave
Heavy to LightBoth transmission and reflection
Boundary feels like a free end to the heavy string
Reflection just like free end, not inverted
Faster, farther from boundary
Longer, “spread out” Wave not inverted
Transmitted wavelength has the same shape except it’s longer in length because it travels faster than the incoming wave.
Slower, so not as far from boundary
Shorter, “bunched up” Inverted wave
Faster, farther from boundary
Longer, “spread out” Same as incoming wave
Light: Glass to Air
Light: Air to Glass
Two slit geometry
Screen
PDL = d sin (d = slit separation)
d sin = m constructive interference
d sin = (m+ 1/2) destructive interference
When the sources (slits) are “in phase”
d
A simpler picture
Screen very far away (L)
Two slits very close together (d)
d sin = m constructive interference
d sin = (m+ 1/2) destructive interference
When the sources (slits) and “in phase”
The m’s
m = 0
m = 1
m = 2
m = 1
m = 2m = 1
m = 0
m = 0
m = 1d sin = md sin = (m+ 1/2)
0 “zeroth order” fringe1 “first order” fringe2 “second order” fringe
Thin Films
Eyeball
The wavelength is different in the film.
Wavelength ()Film thickness (PLD)Index of refraction (n)Phase shifts
film = vacuum /nfilm
Thin Film Problems
Draw picture Consider reflected wave phase shifts
none, one, or both can be shifted
Find in the film Chose m or (m + 1/2) (use in the film)
Constructive or destructive? Phase shifts?
PLD = 2t for thin films
Total internal reflection
Water - index of refraction nW = 1.33
nAsin A = nWsin W Air - index of refraction nA = 1.0
A
W
As W increases, so does A
until A becomes 90°. C is called the “critical angle”. If W is greater that C no light will escape the water and all will be “internally reflected.”
Total internal reflection only happens when light goes from high n to low n and it depends on both n’s!
nAsin 90 = nWsin C ornA = nWsin C
C
Example:What is the critical angle for light traveling from water into air?
n2 = n1sin C
n1 = 1.33
C
n2 = 1.0sin C = n2/n1 = 0.752C = 48.8°
Note that there is no critical angle for light from low index to higher index.
Example:What happens if the angle of incidence is greater than 48.8°?
n2 = n1sin C
n1 = 1.33
1 = 50°
n2 = 1.0
50°
Example:What happens if I place a sheet of glass on the water, ng = 1.5?
n2sin 2 = n1sin 1
n1 = 1.33
1 = 50
n2 = 1.0
ng = 1.5
No internal reflection possible-low to high n!
n2 = n1sin C
1.5sin g = 1.33sin50° g = 42.8°
Now what happens? C = Arcsin1/1.5 = 41.8°
The light reflected back into the glass.
g = 42.8
Diverging Lens-Ray Diagrams
ff
Bend the ray at the middle of the lensIn parallel-out as if from left focus
Also straight through the center of the lens
For lenses (both types) di is positive on the right.Here di will be a negative number. f is negative for diverging lenses.
di
In as if toward right focus-out parallel
Diverging Lens-Ray Diagrams and Math
ff
di
d0 = +12 cm, f = -4 cm find di, m, hi
fdd i
111
0
00 d
d
h
hm ii
Virtual and Real Images
Real: Virtual:
A screen placed at the image will produce an image.
A screen placed at the image will not produce an image.
All image forming rays actually pass through the image.
At most only one image forming ray will pass through the image.
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