1. Today5/1 Questions? Waves (review) phase shifts interference
reftaction
lenses/mirrors
etc..

2. Interference in 2-D Sources “in 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 light
Crest
Trough

3. Interference in 2-D Sources “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

4. Interference in 2D Sources “out of phase”
Crest meets crest and trough meets trough, constructive, loud sound or bright
Crest meets trough and trough meets crest, destructive, no sound or dark
Crest
Trough

5. Interference in 2-D Sources “out of phase”
Constructive at a point if the point is 1/2 farther away from one source
Destructive at a point if the point is the same distance from each source
Crest
Trough

6. Reflections at Boundaries
Four situations
Fixed end
Light to heavy
Free end
Heavy to light

7. Fixed End Reflections Crest turns into trough Leading edge is the same
Same velocity, length, and amplitude
See “Wave Interference” handout for how the string looks during the reflection.

8. Free End Reflections Crest stays a crest Leading edge is the same
Same velocity, length, and amplitude
See “Wave Interference” handout for how the string looks during the reflection.

9. Light to Heavy Both 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
Inverted wave
Shorter, “bunched up”

10. Heavy to Light Both transmission and reflection
Boundary feels like a free end to the heavy string
Reflection just like free end, not inverted
Transmitted wavelength has the same shape except it’s longer in length because it travels faster than the incoming wave.
Faster, farther from boundary
Wave not inverted
Longer, “spread out”

11. Light: Glass to Air
Faster, farther from boundary
Same as incoming wave
Longer, “spread out”
Light: Air to Glass
Slower, so not as far from boundary
Inverted wave
Shorter, “bunched up”

12. Two slit geometry (screen far away)
PLD = d sin (d = slit separation) d 
Screen
PLD  d
(close enough) 

13. Two slit geometry PDL = d sin (d = slit separation) Screen 
d sin = m constructive interference
d sin = (m+ 1/2) destructive interference
When the sources (slits) are “in phase”

14. A simpler picture Two slits very close together (d)
Screen very far away (L) 
d sin = m constructive interference
d sin = (m+ 1/2) destructive interference
When the sources (slits) and “in phase”

15. The m’s d sin = m d sin = (m+ 1/2) 0 “zeroth order” fringe
1 “first order” fringe
m = 0
m = 1
m = 2
2 “second order” fringe
d sin = m
d sin = (m+ 1/2)

16. Thin Films The wavelength is different in the film.
Wavelength () Film thickness (PLD) Index of refraction (n) Phase shifts
film = vacuum /nfilm
Eyeball

17. 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

18. Total internal reflection
Air - index of refraction nA = 1.0
nAsin A = nWsin W
As W increases, so does A 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.” C
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 or nA = nWsin C W
Water - index of refraction nW = 1.33

19. Example: n2 = n1sin C sin C = n2/n1 = 0.752 C = 48.8° C
What is the critical angle for light traveling from water into air?
sin C = n2/n1 = 0.752
n2 = 1.0
C = 48.8° C
Note that there is no critical angle for light from low index to higher index.
n1 = 1.33

20. Example: n2 = n1sin C 50° 1 = 50°
What happens if the angle of incidence is greater than 48.8°?
n2 = 1.0
50°
1 = 50°
n1 = 1.33

21. Example: n2 = n1sin C n2sin 2 = n1sin 1 g = 42.8 1 = 50
What happens if I place a sheet of glass on the water, ng = 1.5?
No internal reflection possible-low to high n!
n2 = 1.0
1.5sin g = 1.33sin50°
g = 42.8°
Now what happens?
C = Arcsin1/1.5 = 41.8°
g = 42.8
ng = 1.5
The light reflected back into the glass.
1 = 50
n1 = 1.33

22. Diverging Lens-Ray Diagrams Bend the ray at the middle of the lens
In parallel-out as if from left focus
In as if toward right focus-out parallel
Also straight through the center of the lens f f di
For lenses (both types) di is positive on the right. Here di will be a negative number. f is negative for diverging lenses.

23. Diverging Lens-Ray Diagrams and Math
d0 = +12 cm, f = -4 cm find di, m, hi f f di

24. Virtual and Real Images
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.

25. Example: f = + 6 cm and - 18 cm lenses are 1 cm apart do = + 12 cm
Math
minus sign because “virtual object”
First lens do = 9, f = 6 di = ?
di = 18
First image m1 = -18/9 = -2
Second lens do = -9, f = -18 di = ?
di = 18
Total m = -2(2) = -4
Second image m2 = -18/-9 = +2
Inverted and real do do di di