Ch 28 Interference and Diffraction in Optics
Lenses in Combination and Corrective Optics
28.2 Double Slit
A laser with wavelength d/8 is shining light on a double slit with slit separation 0.500
mm. This results in an interference pattern on a screen a distance L away from the
slits. We wish to shine a second laser, with a different wavelength, through the same
slits. What is the wavelength λ2 of the second laser that would place its second
maximum at the same location as the fourth minimum of the first laser, if d = 0.500
mm?
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d sinθ = m λ
d: inverse of the grating constant in meters, in our case (non-SI units of mm)
where m is the 1st order maxima, or the 2nd order maxima, etc.
o if you want out of phase (maxima matching to minima), then
o m - ½ corresponds to the 1st minima, when m = 2 then 2 - ½ is the 2nd minima, etc.
we also know sinθ must be equal in both cases if they are the same distance.
4th Minima
d sinθ = (4 - ½) λ1
2nd Maxima
d sinθ = 2 λ2
28.3 Interference from Reflection off a
Soap Film
What is the thinnest soap (nsoap = 1.33) film
that appears black when illuminated with
light with a wavelength of 490 nm?
2 λ2 = (4 - ½) λ1
2 λ2 = (4 - ½) d/8
λ2 = 0.109 mm
The light reflected off the top of the soap has a
half-wave phase shift, while the light that reflects
off the bottom has no phase shift.
v=c/n
v=fλ
c / nair = f λair
f = c / (nair λair)
we also know freq can’t change
c / nsoap =
f
λsoap
c / nsoap = c / (nair λair) λsoap
1 / nsoap = 1 / (1 λair) λsoap
λsoap = λair / nsoap
λsoap = 490nm / 1.33
λsoap = 368 nm
Since the light reflected off the top and bottom of the bubble are 180° out of phase, the
thickness of the bubble must correspond to ½ λsoap
½ λsoap = 368/2
½ λsoap = 184 nm
28.5 Rayleigh's criterion
Resolving Power
sinθd = 1.22 λ/D
sin(1/60°) = 1.22 570x10-9 / D
D = 2.39 mm
If you can read the bottom row of your
doctor's eye chart (λlight = 570 nm), your eye
has a resolving power of one arcminute, equal
to 1/60°. If this resolving power is
diffraction-limited, to what effective
diameter of your eye's optical system does
this correspond?
(The factor 1.22 comes from the fact that we are using a circular
aperture for the diffraction pattern instead of an infinite slit.)
Inversion glasses demo: OP-A-IG
Polarized Light Reflection: OP-H-PR
Diffraction Bench, Pasco: OP-C-DB
Laser Tree Diffraction: OP-C-TD
Speckles on the Wall Demo: OP-D-SW
Color Mixing Demo: OP-F-CM