JEE Main 2024 — 29 January, Shift 2 — Question 55

For $\mathrm{n}^{\text {th }}$ minima $\mathrm{b} \sin \theta=\mathrm{n} \lambda$ ( $\lambda$ is small so

$\sin \theta$ is small, hence $\sin \theta \simeq \tan \theta$ ) $\mathrm{btan} \theta=\mathrm{n} \lambda$

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

$\Rightarrow \mathrm{y}_{\mathrm{n}}=\frac{\mathrm{n} \lambda \mathrm{D}}{\mathrm{b}}$ (Position of

$\mathrm{n}^{\text {th }}$ minima) $\mathrm{B} \rightarrow 1^{\text {st }}$

minima, $\mathrm{A} \rightarrow 3^{\text {rd }}$ minima

$\mathrm{y}_{3}=\frac{3 \lambda \mathrm{D}}{\mathrm{b}}, \mathrm{y}_{1}=\frac{\lambda \mathrm{D}}{\mathrm{b}}$

$\Delta y=y_{3}-y_{1}=\frac{2 \lambda D}{b}$

$3 \times 10^{-3}=\frac{2 \times 6000 \times 10^{-10} \times 0.5}{\mathrm{~b}}$

$\mathrm{b}=\frac{2 \times 6000 \times 10^{-10} \times 0.5}{3 \times 10^{-3}}$

$\mathrm{b}=2 \times 10^{-4} \mathrm{~m}$ $\mathrm{x}=2$