Q137 / 150 · MHT CET 2024 (03 May Shift 2) · Physics

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

Correct answer
A
0.2 mm
B
0.02 mm
C
2 mm
D
20 mm

Solution

The position of nth minima in the diffraction pattern $\begin{aligned} & \mathrm{x}_{\mathrm{n}}=\frac{\mathrm{nD} \lambda}{\mathrm{~d}} \\ & \begin{aligned} \mathrm{x}_3 & -\mathrm{x}_1=(3-1) \frac{\mathrm{D} \lambda}{\mathrm{~d}} \\ & =\frac{2 \mathrm{D} \lambda}{\mathrm{~d}} \\ \mathrm{~d} & =\frac{2 \mathrm{D} \lambda}{\mathrm{x}_3-\mathrm{x}_1} \\ & =\frac{2 \times 0.5 \times 600 \times 10^{-9}}{3 \times 10^{-3}} \\ & =0.2 \mathrm{~mm} \end{aligned} \end{aligned}$

Hence, the correct answer is option: 'A'.

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