Question

White light is used to illuminate the two slits in a Young's double slit experiment. The separation between the slits is d and the screen is at a distance $D(>>d)$ 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. $\lambda =\frac{d^2}{D}$
• B. $\lambda =\frac{2d^2}{D}$
• C. $\lambda =\frac{d^2}{3D}$
• D. $\lambda =\frac{2d^2}{3D}$

Answer 1

Answer: (A), (C)

The correct options are
A $\lambda =\frac{d^2}{D}$
C $\lambda =\frac{d^2}{3D}$

For missing wavelength, destructive interference should take place infront of slits, so minima is formed.
$\therefore \Delta x=\frac{\left(y\right)\times d}{D}=\frac{\left(\frac{d}{2}\right)\times d}{D}=(n+\frac{1}{2})\lambda$
$\frac{d^2}{2D}=(2n+1)\frac{\lambda }{2}$
for $n=0,\lambda =\frac{d^2}{D}$
$n=1\lambda =\frac{d^2}{3D}$