Q133 / 155 · WBJEE 2024 · Physics
In a single-slit diffraction experiment, the slit is illuminated by light of two wavelength $\lambda_1$ and $\lambda_2$. It is observed that the 2 nd order diffraction minimum for $\lambda_1$ coincides with the 3 rd diffraction minimum for $\lambda_2$. Then
- A$\frac{\lambda_1}{\lambda_2}=\frac{2}{3}$
- B$\frac{\lambda_1}{\lambda_2}=\frac{5}{7}$
- Correct answerC$\frac{\lambda_1}{\lambda_2}=\frac{3}{2}$
- D$\frac{\lambda_1}{\lambda_2}=\frac{7}{5}$
Solution
Hint: $d \sin \theta=\mathrm{n} \lambda$
$$
\begin{aligned}
& \mathrm{n}_1 \lambda_1=\mathrm{n}_2 \lambda_2 \\
& \frac{\lambda_1}{\lambda_2}=\frac{\mathrm{n}_2}{\mathrm{n}_1}=3 / 2
\end{aligned}
$$
Hence, the correct answer is option: 'C'.