Young’s Fringes

1. 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

3. A wave model

4. Model intereference

5. 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.

8. 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.

10. 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).

11. 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!

12. 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.

13. 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.

15. 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.

16. Coherent interference of four sources

17. 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.

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