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

s1s1 s2s2 d Along the center line, it is obvious that the distances to two sources are identical.  |r 1 -r 2 | = 0 and constructive int. ● P  dsin  |r 1 - r 2 | = dsin  = m Constructive Int. = (2m + 1) /2Destructive Int. Interference phenomena ↔ Pathlength difference

 s =d(x/h) = m (0, ±, ± 2, …) Constructive (m+1) /2 (± /2, ±3 /2,…) Destructive d(x/h) = m  x = m(h/d)  for constructive int. d h x nd -order bright fringe 2 nd bright fringe

Huygen’s principle: Each point on a wavefront acts as a new Source of identical waves. 0 th 2 nd 1 st 3 rd Coherent light sources by splitting

Interference in thin films x  s = Difference in two routes + 2x = m  constructive = (2m+1) /2 destructive = 2x (when  i << 1) For an arbitrary angle   s = 2x/cos  Half –reflecting planes x

xn Difference in two routes  s = 2x= mconstructive f Wavelength in the film (not in air) v = c/n = f f c = f f = /n

Diffraction Grating d   r = dsin  = m  Constructive provides much clearer and sharper interference pattern and a practical device for resolving spectra.

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, 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, (2006)