KCET · Physics · Wave Optics
A slit of width \(a\) is illuminated by red light of wavelength \(6500 Å\). If the first diffraction minimum falls at \(30^{\circ}\), then the value of \(a\) is
- A \(6.5 \times 10^{-4} \mathrm{~mm}\)
- B \(1.3\) micron
- C \(3250 Å\)
- D \(26 \times 10^{-4} \mathrm{~cm}\)
Answer & Solution
Correct Answer
(B) \(1.3\) micron
Step-by-step Solution
Detailed explanation
Given, \(\lambda=6500 Å=6500 \times 10^{-10} \mathrm{~m}, \theta=30^{\circ}\) According to the diffraction pattern of single slit,
\(a \sin \theta=n \lambda\)
where, \(n=\) order of secondary minima \(=1\)
\(\Rightarrow a \sin 30^{\circ}=1 \times\left(6500 \times 10^{-10}\right)\)
\(\Rightarrow \quad \frac{a}{2}=6500 \times 10^{-10}\)
or
\(\begin{aligned}
a &=13000 \times 10^{-10} \\
&=1.3 \times 10^{-6} \mathrm{~m}=1.3 \text { micron }
\end{aligned}\)
\(a \sin \theta=n \lambda\)
where, \(n=\) order of secondary minima \(=1\)
\(\Rightarrow a \sin 30^{\circ}=1 \times\left(6500 \times 10^{-10}\right)\)
\(\Rightarrow \quad \frac{a}{2}=6500 \times 10^{-10}\)
or
\(\begin{aligned}
a &=13000 \times 10^{-10} \\
&=1.3 \times 10^{-6} \mathrm{~m}=1.3 \text { micron }
\end{aligned}\)
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