Question

In Young's double slit experiment the slits are $0.5\, mm$ apart and the interference is observed on a screen at a distance of $100\, cm$ from the slit. It is found that the $9\,\text{ th}$ bright fringe is at a distance of $7.5\, mm$ from the second dark fringe from the centre of the fringe pattern on same side. Find the wavelength of the light used.

• A. $5000\,\mathring{A}$
• B. $3000\,\mathring{A}$
• C. $7000\,\mathring{A}$
• D. None

Answer 1

Answer: (A)

$\frac{9 D \lambda}{ d }-\frac{3}{2} \frac{ D \lambda}{ d } $
$=7.5\, mm , d =0.5 \times 10^{-6}$
$\frac{ D \lambda}{ d }[9-1.5] $
$=7.5\, mm , d =5 \times 10^{-7}$
$\frac{ D \lambda}{ d }=1\, mm$
$\frac{1 \times \lambda}{0.5 \times 10^{-3}}=1 \times 10^{-3}$
$\Rightarrow \lambda=5000\, \mathring{A}$