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(C) The condition for the $n^{th}$ order diffraction minimum in a single-slit experiment is given by $a \sin 	heta = n \lambda$, where $a$ is the sli

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$\frac{\lambda_1}{\lambda_2} = \frac{3}{2}$

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(C) The condition for the $n^{th}$ order diffraction minimum in a single-slit experiment is given by $a \sin 	heta = n \lambda$, where $a$ is the slit width and $	heta$ is the angle of diffraction.For the $2^{nd}$ order minimum of $\lambda_1$, we have $a \sin 	heta_1 = 2 \lambda_1$.For the $3^{rd}$ order minimum of $\lambda_2$, we have $a \sin 	heta_2 = 3 \lambda_2$.Since the minima coincide, the angles of diffraction are equal, i.e.,$	heta_1 = 	heta_2 = 	heta$.Therefore, $2 \lambda_1 = 3 \lambda_2$.Rearranging the terms, we get $\frac{\lambda_1}{\lambda_2} = \frac{3}{2}$.

In a single-slit diffraction experiment, the slit is illuminated by light of two wavelengths $\lambda_1$ 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:

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