Question

White light is used to illuminate the two slits in YDSE. 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. $\lambda =\frac{b^2}{d}$
• B. $\lambda =\frac{2b^2}{d}$
• C. $\lambda =\frac{b^2}{3d}$
• D. $\lambda =\frac{2b^2}{3d}$

Answer 1

Answer: (A), (C)

The correct options are
A

$\lambda =\frac{b^2}{d}$

C

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

$O_{1}P=y=\frac{b}{2}$

$\Delta x=S_{2}P-S_{1}P=\frac{yb}{d}$

$=\frac{\left(\frac{b^2}{2}\right)}{d}=\frac{b^2}{2d}$

Wavelength are missing for,

$\Delta x=\frac{{\lambda }_1}{2},\frac{3{\lambda }_2}{2},\frac{5{\lambda }_3}{2}$

${\lambda }_1=2\Delta x=\frac{b^2}{d},{\lambda }_2=\frac{2\Delta x}{3}=\frac{b^2}{3d},{\lambda }_3=\frac{2\Delta x}{5}=\frac{b^2}{5d}$