Question

White light is used to illuminate the two slits in Young's double slit experiment. The separation 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. $\lambda =b^2/d$
• B. $\lambda =2b^2/d$
• C. $\lambda =b^2/3d$
• D. $\lambda =2b^2/3d$

Answer 1

Answer: (A), (C)

$\lambda =b^2/3d$

At $P$ (directly infront of $S_1$) , $y=\frac{b}{2}$


$\therefore \text{Path difference,}$
$\Delta x=S_{2}P-S_{1}P=\frac{y\times b}{d}=\frac{\left(\frac{b}{2}\right)\left(b\right)}{d}=\frac{b^2}{2d}$

Those wavelengths will be missing for which
$\Delta x=\frac{{\lambda }_1}{2},\frac{3{\lambda }_2}{2},\frac{5{\lambda }_3}{2}...$

$\therefore {\lambda }_1=2\Delta x=\frac{b^2}{d}$

${\lambda }_2=\frac{2\Delta x}{3}=\frac{b^2}{3d}$

${\lambda }_3=\frac{2\Delta x}{5}=\frac{b^2}{5d}$

$\therefore$ Correct options are (a) and (c).