Whenever two portions of the same light arrive at the eye
by different routes, either exactly or very nearly in the
same direction, the light becomes most when the difference
of the routes is any multiple of a certain length, and the
least intense in the intermediate state of interfering
portions; and this length is different for light of different
colour.
T. Young from a paper to the Royal Society in 1802
Interference phenomena ↔ Pathlength difference
● P
s1
q
d
s2
dsinq
Along the center line, it is obvious that the distances to
two sources are identical.  |r1-r2| = 0 and constructive int.
|r1 - r2| = dsinq = ml
= (2m + 1)l/2
Constructive Int.
Destructive Int.
Ds =d(x/h) =
ml (0, ±l, ±2l, …)
Constructive
(m+1)l/2 (±l/2, ±3l/2,…)
Destructive
d(x/h) = ml  x = m(h/d) l for constructive int.
3
2
1x
0
d
h
2nd-order bright fringe
2nd bright fringe
1
2
3
Coherent light sources by splitting
3rd
2nd
1st
0th
Huygen’s principle: Each point on a wavefront acts as a new
Source of identical waves.
Diffraction Grating
provides much clearer and sharper interference pattern
and a practical device for resolving spectra.
Dr = dsinq = ml  Constructive
d
q
632.8 nm red beam of a helium-neon laser through a 600 lines/mm diffraction grating
(1 mm/ 600) sin a= (n=1)(632.8 nm)
Then sin a ~ distance between
spots / distance to screen.
HITT:
A laser through a grid of slits, 0.0625 mm each, 0.25 mm separations between
their centers. This picture was taken in the teaching labs of the Ben Gurion
University Physics Department
Find wavelength of the light (in the few hundred nm range)?
X ray Crystallography
• Q: How do you determine the atomic
structure of a crystal? A: interference
patterns
Panel A, peaks vs. angle (ignore panel B, that has to do
with their determination of the structure)
material: pyrite (FeS2) X-ray diffraction
Nature Materials 5, 647 - 652 (2006)