A single slit of width 1 micrometre is illuminated by monochromatic plane waves and produces a central diffraction maximum of angular width 60 deg (i.e. 30 deg on each side). A second identical slit is then made beside the first, and Young's interference fringes are observed on a screen 50

Question

A single slit of width 1 micrometre is illuminated by monochromatic plane waves and produces a central diffraction maximum of angular width 60 deg (i.e. 30 deg on each side). A second identical slit is then made beside the first, and Young's interference fringes are observed on a screen 50 cm away. If the measured fringe width is 1 cm, find the separation between the centres of the two slits.

Accepted Answer

25 micrometre. Central maximum half-angle = 30 deg gives a*sin(30) = lambda, so lambda = (1*10⁻⁶)*(0.5) = 0.5*10⁻⁶ m = 5000 Angstrom. For double-slit, beta = lambda*D/d => d = lambda*D/beta = (0.5*10⁻⁶ * 0.5)/(0.01) = (0.25*10⁻⁶)/0.01 = 2.5*10⁻⁵ m = 25 micrometre.

Solution

Related JEE Advanced Physics questions