Question

White light is used for illuminating the two slits in a Young's double slit experiment. The separation between the slits is $b$ and the screen is at a distance $d(d>>b)$ from the slits. At a point on the screen directly in front of one of the slits certain wavelengths are missing. One of the missing wavelength is

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

Answer 1

The correct option is A $\frac{b^2}{d}$

Destructive interference has occurred at that point. Its distance from centre is $x=\frac{b}{2}$

For dark fringes, $x=\frac{(2n-1)\lambda d}{2b}\Rightarrow \lambda =\frac{b^2}{(2n-1)d}$

For first dark fringes, $n=1,\therefore \lambda =\frac{b^2}{d}$