Question

In a Young’s double-slit experiment, the separation between the slits is d, distance between the slit and screen is exactly infront of each slit.is D Then, the possible wavelength(s) used in the experiment are

• A. $\frac{d^2}{D};\frac{d^2}{2D};\frac{d^2}{3D}$
  
• B. $\frac{d^2}{D};\frac{d^2}{3D};\frac{d^2}{5D}$
  
• C. $\frac{d^2}{2D};\frac{d^2}{4D};\frac{d^2}{6D}$
• D. None of these

Answer 1

The correct option is C $\frac{d^2}{2D};\frac{d^2}{4D};\frac{d^2}{6D}$

Path diff x = $\frac{Xd}{D}$
$X=\frac{d}{2}$ ; $n=1$
$n\lambda =\frac{Xd}{D}$
$\lambda =\frac{\frac{d}{2}\times d}{D}=\frac{d^2}{2D}$
When n = 2
$\lambda =\frac{d^2}{2D}$
$\therefore$ $\frac{d^2}{2D};\frac{d^2}{4D};\frac{d^2}{6D}$