Q.In Fraunhoffer diffraction by a narrow slit, a screen is placed at a distance of 2 m from the lens to obtain the diffraction pattern. If the slit width is 0.2 mm and the first minimum is 5 mm on either side of the central maximum, find the wavelength of light.

[!TLDR] The first minimum of single-slit diffraction sits at $y=\lambda D/a$; solving for $\lambda$ with $y=5$ mm, $a=0.2$ mm, $D= …

The first diffraction minimum of a single slit occurs at angular position $\theta$ where $a\sin\theta=\lambda$ (Section 7.9.3, taking $n=1$ for the first minimum); using the small-angle approximation valid since $D\gg a$, $\sin\theta\approx y/D$, so the minimum's LINEAR distance from the centre is $y=\lambda D/a$. Rearranging for the unknown wavelength: $\lambda=\dfrac{ya}{D}$. Substituting the given values -- $y=5\text{ mm}=5\times10^{-3}$ m, $a=0.2\text{ mm}=2\times10^{-4 …

Use the single-slit first-minimum condition $y=\lambda D/a$ (from $a\sin\theta=\lambda$ with the small-angle approximation …

Using the double-slit bright-fringe formula ($y=n\lambda D/d$) instead of the single-slit diffraction MINIMUM formula, or forgetting to convert the given slit width …