MHT CET · Physics · Wave Optics
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
- A 0.2 mm
- B 0.02 mm
- C 2 mm
- D 20 mm
Answer & Solution
Correct Answer
(A) 0.2 mm
Step-by-step Solution
Detailed explanation
The position of nth minima in the diffraction pattern
\(\begin{aligned}
& \mathrm{x}_{\mathrm{n}}=\frac{\mathrm{nD} \lambda}{\mathrm{~d}} \\
& \begin{aligned}
\mathrm{x}_3 & -\mathrm{x}_1=(3-1) \frac{\mathrm{D} \lambda}{\mathrm{~d}} \\
& =\frac{2 \mathrm{D} \lambda}{\mathrm{~d}} \\
\mathrm{~d} & =\frac{2 \mathrm{D} \lambda}{\mathrm{x}_3-\mathrm{x}_1} \\
& =\frac{2 \times 0.5 \times 600 \times 10^{-9}}{3 \times 10^{-3}} \\
& =0.2 \mathrm{~mm}
\end{aligned}
\end{aligned}\)
\(\begin{aligned}
& \mathrm{x}_{\mathrm{n}}=\frac{\mathrm{nD} \lambda}{\mathrm{~d}} \\
& \begin{aligned}
\mathrm{x}_3 & -\mathrm{x}_1=(3-1) \frac{\mathrm{D} \lambda}{\mathrm{~d}} \\
& =\frac{2 \mathrm{D} \lambda}{\mathrm{~d}} \\
\mathrm{~d} & =\frac{2 \mathrm{D} \lambda}{\mathrm{x}_3-\mathrm{x}_1} \\
& =\frac{2 \times 0.5 \times 600 \times 10^{-9}}{3 \times 10^{-3}} \\
& =0.2 \mathrm{~mm}
\end{aligned}
\end{aligned}\)
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