In a single-slit diffraction experiment, the first minimum for a light of wavelength 500text{ nm} coincides with the first minimum for a light of wav…

The condition for the first minimum in single-slit diffraction is $a \sin\theta = \lambda$. Since both first minima coincide, their angle $\theta$ is the same. Thus, $a \sin\theta = 500\text{ nm}$ and $a \sin\theta = \lambda$, giving $\lambda = 500\text{ nm}$ (assuming the question implies they coincide at the same position, which requires identical wavelengths if slit width and distance are identical, or maybe it's a trick question? Wait, if they are different wavelengths, their first minima cannot coincide at the exact same location unless slit width varies or order changes. Let's re-read: 'first minimum for a light of wavelength 500 nm coincides with the first minimum for a light of wavelength $\lambda$...'. If slit $a$ and distance $D$ are same, $y = \lambda D / a$. For $y$ to be the same, $\lambda$ must be same. Thus $\lambda = 500\text{ nm}$.)