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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 • 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? • 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 • 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 • 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 • 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 • 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 • 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 • 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.
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.
The Young bright fringes are much narrower than before. • Thus with many light sources, the Young fringes become brighter and sharper!
