450 Week 13: Interference and Diffraction
Diffraction Minima
m sin(θm) θm
1 14 sin−^1( 1
4)
= 0. 25268
2 24 sin−^1( 1
2)
= 0. 52360
3 34 sin−^1( 3
4)
= 0. 84806
4 44 sin−^1 (1) = 1. 57079
Interference Maxima
m sin(θm) θm
0 0. 0 sin−^1 (0.0) = 0. 00000
1 18 sin−^1( 1
8)
= 0. 12532
2 28 sin−^1( 1
4)
= 0. 25268
3 38 sin−^1( 3
8)
= 0. 38439
4 48 sin−^1( 1
2)
= 0. 52360
5 58 sin−^1( 5
8)
= 0. 67513
6 68 sin−^1( 3
4)
= 0. 84806
7 78 sin−^1( 7
8)
= 0. 94843
8 88 sin−^1 (1) = 1. 57079
Interference Minima
m sin(θm) θm
0 161 sin−^1( 1
16)
= 0. 62540
1 163 sin−^1( 3
16)
= 0. 18862
2 165 sin−^1( 5
16)
= 0. 31782
3 167 sin−^1( 7
16)
= 0. 45282
4 169 sin−^1( 9
16)
= 0. 59741
5 1116 sin−^1( 11
16)
= 0. 75804
6 1316 sin−^1( 13
16)
= 0. 94843
7 1516 sin−^1( 15
16)
= 1. 21538
Table 7: Diffraction minima, interference maxima, and interference minima for a single slit of width
a= 4λ.
lens of a camera, or the lens of a telescope – it doesn’t really matter what the aperture
is as long as it is circular and symmetric.
The occurence of a lens in the aperture doesn’t affect the diffraction –every raygets
bent by the lens to be focussed on the screen according to the angles in the diffraction
patter, so the point-like object is focussed down not to a point, but to a circular dot. The
sizeof the dot is basically determined by the angle of the first diffraction minimum, with
smaller wavelengths being better resolved. Indeed, everything welearned in geometric
optics, where source points on the object were mapped directly toimage points by the
lens, is what true physical optics predicts in the limit ofinfinitely short wavelengths(or
more practically, wavelengths that are “infinitely” short comparedto the aperture or
length scales of the imaging apparatus)^130.
We can then ask: Suppose we are photographing a section of sky with our telescope and
see a large, slightly asymmetric blob of “white” on our photograph corresponding to a(^130) This is actually avery important result, one worth reinforcing for possible math or physics majors. Geometric
optics is the small wavelength limit of physical (wave) optics. Similarly,classical mechanicsis the small wavelength
limit of quantum (wave) mechanics! This answers one of the most important of questions from the Enlightenment
- how light can behave like a particle (geometric) and wave (physical) at the same time, and extends it with the
surprising result that microscopic objects like electronsand protons behaveexactly the same way, with the same
kind of schizophrenia producing particle-like behavior inone context or measurement apparatus, wave-like behavior
in another.