Physics · Ch 6 — Optics
Interference with Polychromatic Light
Interference with Polychromatic Light
When polychromatic (white) light is used instead of a single wavelength in an interference experiment, coloured fringes of varying width appear on the screen, since different colours have different wavelengths and hence different fringe widths . The central (zeroth-order) fringe, however, always stays sharply bright and white, because at the exact centre every colour has zero path difference simultaneously, so only constructive interference is possible there for every wavelength at once; away from the centre, each colour's bright fringes fall at slightly different positions, so the fri …
Worked out. Two wavelengths, 560 nm and 420 nm, are used together in Young's double-slit experiment with d = 3 mm and D = 1 m. Since fringe position y(n) = n lambda D/d, and 420 is 3/4 of 560, the nth-order bright fringe of the 560 nm light coincides with the (n+1)th order bright fringe of the 420 nm light when n times 560 equals (n+1) times 420, which (after simplifying the ratio 560/420 = 4/3) is satisfied first at n = 3 (so the 3rd order of 560 nm coincides with the 4th order of 420 nm). Substituting n = 3 into y = n lambda D/d for the 560 nm light gives y = 3 times 560e-9 times 1 / 3e-3 = 0.560e-3 m = 0.560 mm -- the smallest distance from the centre at which the two independent fringe patterns li …