Question

White light is used to illuminate 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 (>> 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)

At P (directly infront of $S_1$ ) y = b / 2
$\therefore$ Path difference,
$\Delta X=S_{2}P-S_{1}P=\frac{y.(b)}{d}=\frac{\left(\frac{b}{2}\right)(b)}{d}=\frac{b^2}{2d}$
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).