A screen is placed at 50 cm from a single slit, which is illuminated with light of wavelength 600 nm. If…
A screen is placed at 50 cm from a single slit, which is illuminated with light of wavelength 600 nm. If separation between the $1^{\text {st }}$ and $3^{\text {rd }}$ minima in the diffraction pattern is 3 mm then slit width is
0.2 mm
0.02 mm
2 mm
20 mm
Solution
The position of nth minima in the diffraction pattern
$\begin{aligned}
& \mathrm{x}_{\mathrm{n}}=\frac{\mathrm{nD} \lambda}{\mathrm{~d}} \\
& \begin{aligned}
\mathrm{x}_3 & -\mathrm{x}_1=(3-1) \frac{\mathrm{D} \lambda}{\mathrm{~d}} \\
& =\frac{2 \mathrm{D} \lambda}{\mathrm{~d}} \\
\mathrm{~d} & =\frac{2 \mathrm{D} \lambda}{\mathrm{x}_3-\mathrm{x}_1} \\
& =\frac{2 \times 0.5 \times 600 \times 10^{-9}}{3 \times 10^{-3}} \\
& =0.2 \mathrm{~mm}
\end{aligned}
\end{aligned}$