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: (C)

$\lambda=b^2/3d$

Answer 2

At P (directly infront of $S_1$ ) y = b / 2
$\therefore$ Path difference,
$\Delta X=S_2 P-S_1 P=\frac{y.(b)}{d}=\frac{\big(\frac{b}{2}\big)(b)}{d}=\frac{b^2}{2d}$
Those wavelengths will be missing for which
\hspace25mm \Delta X=\frac{\lambda_1}{2},\frac{3 \lambda_2}{2},\frac{5 \lambda_3}{2}...
\therefore \hspace25mm \lambda_1=2 \Delta x=\frac{b^2}{d}
\hspace25mm \lambda_2=\frac{2 \Delta x}{3}=\frac{b^2}{3d}
\hspace25mm \lambda_3=\frac{2 \Delta x}{5}=\frac{b^2}{5d}
$\therefore$ Correct options are (a) and (c).