Question

In Young's double slit experiment,$1^{st}$ dark fringe occurs directly opposite a slit. Wavelength of light used is

• A. $\frac{d^2}{D}$
• B. $\frac{d}{D}$
• C. $\frac{D^2}{d}$
• D. $\frac{2d^2}{D}$

Answer 1

Answer: (A)

$\frac{d^2}{D}$

Answer 2

Condition for dark fringes
$\Delta x = \left(n + \frac{1}{2}\right)\lambda$
Also, $\Delta x=d \tan \theta = d \tan\theta = d \frac{y }{\Delta }$
$\therefore \, d \frac{y}{D} = \left(n +\frac{1}{2}\right)\lambda$
For $n =0, Y = \frac{d}{2}$
$. \Rightarrow \frac{d . \left(\frac{d}{2}\right)}{D} = \frac{\lambda}{2} or, \lambda = \frac{d^{2}}{D}$