1. Physics 102: Lecture 20
Interference 1

2. Phys 102 recent lectures Light as a wave Light as a ray
Lecture 14 – EM waves
Lecture 15 – Polarization
Lecture 20 & 21 – Interference & diffraction
Light as a ray
Lecture 16 – Reflection
Lecture 17 – Spherical mirrors & refraction
Lecture 18 – Refraction & lenses
Lecture 19 – Lenses & your eye

3. Constructive Interference
Superposition
Constructive Interference t +1 -1 + t +1 -1
In Phase t +2 -2

4. Destructive Interference
Superposition
Destructive Interference +1 t -1 + +1
Out of Phase
180 degrees t -1 t +2 -2

5. ACT: Superposition + Different f
1) Constructive 2) Destructive 3) Neither

6. Interference Requirements
Need two (or more) waves
Must have same frequency
Must be coherent (i.e. waves must have definite phase relation)

7. Demo: Interference for Sound …
For example, a pair of speakers, driven in phase, producing a tone of a single f and l:
hmmm… I’m just far enough away that l2-l1=l/2, and I hear no sound at all! l1 l2
Demo 440 Sound Interference
But this won’t work for light--can’t get coherent sources

8. Interference for Light …
Can’t produce coherent light from separate sources. (f  1014 Hz)
Need two waves from single source taking two different paths
Two slits
Reflection (thin films)
Diffraction*
Today’s lecture
Next lecture

9. Young’s double slit/rays
Monochromatic light travels through 2 slits onto a screen
What pattern emerges on the screen?
Bright spots
Shadow
This is not what is actually seen!

10. Young’s double slit/Huygens
Recall Huygens’ principle: Every point on a wave front acts as a source of tiny wavelets that move forward. •
Bright and dark spots on screen!
Constructive = bright •
Destructive = dark
Wave crests in phase = constructive interference

11. Young’s double slit: Key idea
Consider two rays traveling at an angle q: • • θ
Bottom ray travels a little further (2l in this case)
Key for interference is this small extra distance.

12. Young’s double slit: Quantitative
Consider two rays traveling at an angle q
Assume screen is very far away (L>>d): ≈ ≈ θ θ d ≈
m = +2
Path length difference = dsin(q) L
Constructive: dsin(q) = ml
Destructive: dsin(q) = (m+1/2)l
where m = 0, 1, 2
Need l < d

13. Young’s double slit: Quantitative
Assume screen is very far away (L>>d), angles q are small:
m = 0
m = +1
m = -1
m = -2
m = +2 y θ θ d
dsin(q) L
sin(q)  tan(q) = y/L
Constructive: dsin(q) = ml
Destructive: dsin(q) = (m+1/2)l
y ≈ mlL/d
y ≈ (m+1/2)lL/d
m = 0, 1, 2

14. ACT: Preflight 20.3
When this Young’s double slit experiment is placed under water, the separation y between minima and maxima:
m = 0
m = +1
m = -1
m = -2
m = +2 y θ θ d
dsin(q) L
1) increases 2) same 3) decreases

15. Preflight 20.2
In the Young double slit experiment, is it possible to see interference maxima when the distance between slits is smaller than the wavelength of light?
1) Yes 2) No

16. Thin Film Interference
Light is incident normal to a thin film
Note: angles exaggerated for clarity 1 2
n0=1.0 (air) t
n1 (thin film) n2
Demo 70 soap film
Get two waves by reflection off two different interfaces: interference!
Ray 2 travels approximately 2t further than ray 1.

17. Reflection & Phase Shifts
Upon reflection from a boundary between two transparent materials, the phase of the reflected light may change.
Reflected
Reflected
Incident
Incident n1 n1 n2 n2
Refracted
Refracted
If n1 > n2 – no phase change upon reflection
If n1 < n2 – 180º phase change upon reflection (shift by l/2)

18. Note: this is wavelength in film! (lfilm= lo/n1)
Thin Film Summary
Determine d, number of extra wavelengths for each ray. 1 2
n = 1.0 (air)
n1 (thin film) t n2
This is important!
Reflection
Distance
Note: this is wavelength in film! (lfilm= lo/n1)
Ray 1: d1 = 0 or ½
+ 0
Ray 2: d2 = 0 or ½
+ 2 t/ lfilm
If |d2 – d1| = 0, 1, 2, 3 … (m) constructive
If |d2 – d1| = ½ , 1 ½, 2 ½ …. (m + ½) destructive

19. ACT: Thin Film Practice
Blue light (l0 = 500 nm) incident on a glass (n1 = 1.5) cover slip (t = 167 nm) floating on top of water (n2 = 1.3). 1 2
n = 1.0 (air)
n1 (thin film) t n2
A) d1 = 0 B) d1 = ½ C) d1 = 1
What is d1, the total phase shift for ray 1

20. Thin Film Practice Example
Blue light (l0 = 500 nm) incident on a glass (n1 = 1.5) cover slip (t = 167 nm) floating on top of water (n2 = 1.3). 1 2
n = 1.0 (air)
n1 (thin film) t n2
Is the interference constructive or destructive or neither?
d1 =
d2 =
Phase shift = |d2 – d1| =

21. ACT: Thin Film Practice II
Example
Blue light (l0 = 500 nm) incident on a glass (n1 = 1.5) cover slip (t = 167 nm) floating on top of plastic (n2 = 1.8). 1 2
n = 1.0 (air)
n1 (thin film) t n2
Is the interference : 1) constructive 2) destructive 3) neither?
d1 =
d2 =
Phase shift = |d2 – d1| =