Diffraction grating slit spacing formula Steps: - Identify the diffraction grating equation: $d \sin \theta = m \lambda$, where $d$ is slit spacing, $m = 3$ (order), $\lambda = 550 \times 10^{-9}$ m. - Calculate $\theta \approx \tan^{-1}(x / L)$, with $x = 0.75$ m, $L = 3.5$ m, so $\theta \approx \tan^{-1}(0.214)$, and $\sin \theta \approx x / L = 0.214$ (small-angle approximation). - Solve for $d \approx m \lambda L / x = 3 \times 5.5 \times 10^{-7} \times 3.5 / 0.75 = 7.7 \times 10^{-6}$ m. - Verify approximation: exact $\sin \theta \approx 0.209$, yielding $d \approx 7.9 \times 10^{-6}$ m, close to 7.7 × 10^{-6} m. Why B is correct: - Matches the grating equation solution for third-order maximum position. Why the others are wrong: - A: Underestimates $d$ by using first-order or incorrect approximation. - C: Zero spacing impossible; violates grating diffraction condition. - D: Same as C; zero …