Question

White light is used to illuminate the two slits in Young's double slit experiment. The distance between the slits is b and the screen is at a distance d (>> b) from the slits. At a point on the screen directly in front of one of the slits, certain wavelengths are missing. Some of these missing wavelengths are

• A. $\lambda =\frac{b^2}{2d}$
  
• B. $\lambda =\frac{2b^2}{d}$
  
• C. $\lambda =\frac{b^2}{3d}$
  
• D. $\lambda =\frac{2b^2}{3d}$

Answer 1

The correct option is C

$\lambda =\frac{b^2}{3d}$

At a point on the screen directly in front of one of the slits, the path difference is $\frac{b}{2}$
For a dark fringe to occur at that point,
$\frac{b}{2}=(m+\frac{1}{2})\frac{D\lambda }{b};m=0,1,2,3,....etc$
Hence, $\lambda =\frac{b^2}{(2m+1)D}$
For m = 1, $\lambda =\frac{b^2}{3D}$