Whenever two portions of the same light arrive at the eye by different routes, either exactly or...

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

s1

s2

d

Along the center line, it is obvious that the distances to two sources are identical. |r1-r2| = 0 and constructive int.

● P

dsin

|r1 - r2| = dsin = m Constructive Int. = (2m + 1)/2 Destructive 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

x0

1

1

2

2

3

32nd-order bright fringe

2nd bright fringe

Huygen’s principle: Each point on a wavefront acts as a newSource of identical waves.

0th

2nd

1st

3rd

Coherent light sources by splitting

Diffraction Grating

d

r = dsin = m Constructive

provides much clearer and sharper interference patternand 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, 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)