1. Geometry of Young’s Double Slit Experiment
Particle theory
What actually happened (wave theory) X
d sinθ = m
tanθ = L

2. Where d = distance between the slits θ = angular separation
m = order maximum (bright bands)
 = wavelength
X = distance from the zeroth order maximum to the mth order maximum
L = distance from the slits to the screen
m=0
x for m=5
m=5
m=5

3. Single slit diffractionX
w sinθ = m
tanθ = L
Where
w = width of the slit
θ = angular separation
m = order minimum (dark bands)
 = wavelength
X = distance from the center of the central bright band to the mth order minimum
L = distance from the slits to the screen
x for m=3
m=3
m=3

4. Diffraction grating – has more than two slits
grating constant – number of slits per unit length
thus d = (grating constant)-1
Example: if the grating constant is 717 lines per mm
d = x 10-3 mm

5. Units d and  must match !!!!!!!!!!!! w and  must match !!!!!!!!!!!!
color
wavelength
red
 690 nm
orange
 620 nm
yellow
 580 nm
green
 530 nm
blue
 450 nm
violet
 390 nm
d and  must match !!!!!!!!!!!!
w and  must match !!!!!!!!!!!!
X and L must match !!!!!!!!!!!!
Calculator must be in degrees!!!
2.48 mm 2) 297 nm
3) 3357 lines/cm 4) 4 : 1
5) 1.8° 6) 4.32 x 10-5 m
7) 1.72 cm 8) 84.5 nm
9) green (532 nm)

6. Thin Film Interference

7. Thin Film Interference

8. Thin Film Interference

9. Thin Film Interference
Ray 1 travels into the film and back it travels 2t (twice the thickness of the film). The path difference between the rays when they come out of the film is 2t.

10. Condition for Constructive Interference:
The reflected rays coming out of the film (5) and the rays that reflected on the film interface with the air(2), must have a path difference of an integer multiple of l/2. This is because (2) flipped going from a less dense to a more dense medium. Note: l is the wavelength in the film.

11. Condition for Constructive Interference
Path Difference= 2t =#lfilm /2
where # =1,3, 5…
t is the thickness of the film. minimum thickness occurs when # = 1.

12. Problem
Calculate the minimum thickness of a soap bubble that results in constructive interference when a light of wavelength 500nm shines on it. Answer: 93.7 nm