Question

In a Young's double-slit experiment, the angle that locates the second dark fringe on either side of the central bright fringe is 7.2°. Find the ratio d/λ of the slit separation d to the wavelength λ of the light.

Answer 1

(m+1/2)/sin(theta) = d/lambda where m=1

Answer 2

tan(α/2) =x/L => x=L tan(α/2)
Coordinate of the second dark fringe is
x=(2k+1)Lλ/d
L tan(α/2)= (2k+1)Lλ/d

d/λ =(2k+1)/tan(α/2)= (2•2+1)/tan3.6°=79.5