QJEEM24Ph75d6: JEE Main 2024 Physics - Class 12 JEEM24Ph75d6 Solution: In a single slit diffraction pattern, a light of wavelength…

For $\mathrm{n}^{\text {th }}$ minima

$\mathrm{b} \sin \theta=\mathrm{n} \lambda$

( $\lambda$ is small so $\sin \theta$ is small, hence $\sin \theta \simeq \tan \theta$ )

$\mathrm{btan} \theta=\mathrm{n} \lambda$

$\mathrm{b} \frac{\mathrm{y}}{\mathrm{D}}=\mathrm{n} \lambda$

$\Rightarrow \mathrm{y}_{\mathrm{n}}=\frac{\mathrm{n} \lambda \mathrm{D}}{\mathrm{b}}\left(\text { Position of } \mathrm{n}^{\mathrm{th}}\right. \text { minima) }$

$\begin{aligned}& \mathrm{B} \rightarrow 1^{\text {st }} \text { minima, } \mathrm{A} \rightarrow 3^{\mathrm{rd}} \text { minima } \\& \mathrm{y}_3=\frac{3 \lambda \mathrm{D}}{\mathrm{b}}, \mathrm{y}_1=\frac{\lambda \mathrm{D}}{\mathrm{b}} \\& \Delta \mathrm{y}=\mathrm{y}_3-\mathrm{y}_1=\frac{2 \lambda \mathrm{D}}{\mathrm{b}} \\& 3 \times 10^{-3}=\frac{2 \times 6000 \times 10^{-10} \times 0.5}{\mathrm{~b}} \\& \mathrm{~b}=\frac{2 \times 6000 \times 10^{-10} \times 0.5}{3 \times 10^{-3}} \\& \mathrm{~b}=2 \times 10^{-4} \mathrm{~m} \\& x=2\end{aligned}$