Question

In a Young's double-slit experiment the wavelength of light used is 489 nm (in vacuum), and the separation between the slits is 2.4 × 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) wave length /2
where d is separation between the slits
For bright fringe , d sin theta= m x wave length .
(a)For m=0 i.e. first dark fringe, d sin theta=wave length / 2
sin theta= 489 x 10 ( - 9 ) / 2.40 x 10-6/2 = 106.2x 10 ( -3)
angle=6.1 degree
(b)For m=1 i.e. first bright fringe,d sin theta=wave length
angle=12.3 degree
(c)For m=1 i.e second dark fringe ,d sin theta=3wave length / 2
angle=18.6 degree
(d)For m=2 i.e.second bright fringe,d sin theta=2wave length
angle=24.8 degree