Diffraction grating maxima on semicircular screen Steps: - The diffraction grating equation is $d \sin \theta = m \lambda$ for bright fringes, where $m = 0, \pm 1, \pm 2, \dots$. - A total of 9 bright dots means the central maximum ($m=0$) plus 4 orders on each side ($m = \pm 1$ to $\pm 4$), so maximum order $m_\text{max} = 4$. - The semicircular screen spans $-90^\circ \leq \theta \leq 90^\circ$, so $\sin \theta \leq 1$. - For exactly 9 dots, the $m=4$ fringes are visible ($\sin \theta_4 < 1$) and the $m=5$ fringes are at the edge ($\sin \theta_5 = 1$), giving $d = 5\lambda = 5 \times 5.0 \times 10^{-7} = 2.5 \times 10^{-6}$ m. Why A is correct: - $d = 5\lambda$ places the $m=5$ order at $\theta = 90^\circ$ (screen edge, not counted as a dot), limiting visible orders to $m_\text{max}=4$ for 9 total dots. Why the others are wrong: - B: $d=4\lambda$ places $m=4$ at $90^\circ$ (not counted), yielding only 7 dots ($m_\text{max}=3$). - C: $d=8\lambda$ allows $m_\text{max}=7$ ($\sin \theta_7 <1$), yielding 15 dots. …