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

Path difference on the screen at a distance $y$ from central maxima=$\frac{yb}{d}$.

Hence path difference at a point directly in front of a slit=$\frac{\left(\frac{b}{2}\right)b}{d}=\frac{b^2}{2d}$

For some wavelength to be missing, some of its odd multiple of half its wavelength must be equal to the above path difference.

Hence, $\frac{b^2}{2d}=(m+\frac{1}{2})\lambda$

For $m=0,\lambda =\frac{b^2}{d}$

For $m=1,\lambda =\frac{b^2}{3d}$