Question

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

• A. $\frac{b^2}{d}$,$\frac{b^2}{3d}$
• B. $\frac{b^2}{d}$,$\frac{b^2}{4d}$
• C. $\frac{b^2}{2d}$,$\frac{b^2}{3d}$
• D. $\frac{b^2}{2d}$,$\frac{b^2}{4d}$

Answer 1

The correct option is A $\frac{b^2}{d}$,$\frac{b^2}{3d}$

$\delta =\frac{\left(\frac{b}{2}\right)b}{d}=\frac{b^2}{2d}$
For missing wavelength, $\delta =\frac{{\lambda }_1}{2},\frac{3{\lambda }_2}{2},\frac{5{\lambda }_3}{2},\frac{7{\lambda }_4}{2}$
So, $\frac{{\lambda }_1}{2}=\frac{b^2}{2d}\Rightarrow {\lambda }_1=\frac{b^2}{d}$
$\frac{3\lambda 2}{2}=\frac{b^2}{2d}\Rightarrow {\lambda }_2=\frac{b^2}{3d}$