Question

In a Young's double-slit experiment the wavelength of light used is 457 nm (in vacuum), and the separation between the slits is 1.7 × 10-6 m. Determine the angle that locates (a) the dark fringe for which m = 0, (b) the bright fringe for which m = 1, (c) the dark fringe for which m = 1, and (d) the bright fringe for which m = 2.

Answer 1

For dark fringe , d sin theta=(2m + 1) wavelength /2

where d is separation between the slits

For bright fringe , d sin theta= m x wavelength .

(a)For m=0 i.e. first dark fringe, d sin theta=wavelength / 2

sin theta= 457 x 10 ( - 9 ) / 1.70 x 10-6/2 = 106.2x 10 ( -3)

angle=7.72 degrees

(b)For m=1 i.e. first bright fringe,d sin theta=wavelength

angle=15.59 degrees

(c)For m=1 i.e second dark fringe ,d sin theta=3wavelength / 2

angle=23.78 degrees

(d)For m=2 i.e.second bright fringe,d sin theta=2wavelength

angle=32.52 degrees