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Young’s Fringes. A single monochromatic point source . Split the light front into two sub-fronts to get two coherent sources. One can do this by two parallel, narrow slits.

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young s fringes
Young’s Fringes
  • A single monochromatic point source.
  • Split the light front into two sub-fronts to get two coherent sources.
    • One can do this by two parallel, narrow slits.
    • If the slits are equidistant from the source, each wave-front reaches both slits at the same time: they are in-phase at the two slits.
  • At large distances from these coherent sources, there are many constructive and destructive interference patterns
how to see young s fringes
How to see Young’s fringes?
  • Place a screen far from the sources
  • Interpose a lens between the sources and screen.
  • Wherever the interference is constructive the screen will be bright; where it’s destructive, the screen will be dark.
  • These regions of alternating bright and dark intensity are called interference fringes.
spacing between the fringes
Spacing between the fringes
  • The fringes not only demonstrate the wave nature of light, they also allow its tiny wavelength to be measured!
    • The wavelength is .
    • The distance between the two slits s1 and s2 is d.
    • The distance between the source screen and the observation screen is D.
    • The extra distance that the light passing through s1 travels is d sinθ.
conditions for bright and dark fringes
Conditions for bright and dark fringes
  • When this extra distance is equal to an integer multiple of the wavelength, we have a constructive interference (bright)

d sinθ = n  (n=0, 1, 2,…)

  • When it is half-integer multiple of , we have a destructive interference (dark).
spacing between fringes
Spacing between fringes
  • For two neighboring bright lines, the angles differ byΔθ=/d.
  • The spacing between the fringes is

It is equal to the wavelength multiplied by an amplification number

for d=1mm, D=1m

D/d = 1000!

qualitative relations
Qualitative relations
  • As d increases the spacing between the fringes gets smaller. Therefore to see large fringes, one must have very small d.
  • For a larger wavelength, one needs a large path difference to have a change of phase, the distance between fringes is larger.
  • If the screen is further, for a fixed angle, the spacing between the fringes gets larger.
white light fringes
White-light fringes
  • Each color contained in the white light interferes only with itself, and the white light fringe pattern is the additive mixture of the fringes in the various spectral colors.
  • The central fringe is white.
  • The next bright fringe is colored (like a rainbow) ranging from yellow to blue.
interference of many coherent sources
Interference of many coherent sources
  • Consider many monochromatic, coherent, in-phase sources on the same line with equal distance between them.
  • When the neighboring sources produce a constructive interferences, all sources interfere constructively, producing very bright lines at the same places where the Young fringes are seen.
slide17

However, we get many destructive interferences:

  • A source can have destructive interference with the nearest neighbor, or the next-to-nearest neighbor, or NNN neighbor etc.
    • For example, with 100 sources, 1 is out of phase with 51, 2 is out of phase with 52, etc. In this case, the first dark fringes occur at 1/50 distance between the Young fringes, because the sources responsible are 50 times the neighboring distance.
slide18

The Young bright fringes are much narrower than before.

  • Thus with many light sources, the Young fringes become brighter and sharper!