Light from a laser strikes a diffraction grating that has 6500 grooves per centimeter.The interference pattern is observed on a wall 1.00 m from the grating.If the wavelength of the laser light is 454 nm,how far from the central maximum is the first order maximum?

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Quizplus · Accepted Answer

The distance to the first order maximum can be calculated using the formula for diffraction grating: $d \sin \theta = m \lambda$. Here, $d = \frac{1}{6500 \text{ cm}^{-1}} = 1.54 \times 10^{-6} \text{ m}$, $m = 1$, and $\lambda = 454 \times 10^{-9} \text{ m}$. Solving for $\sin \theta$ gives $\sin \theta = \frac{1 \times 454 \times 10^{-9}}{1.54 \times 10^{-6}}$. The distance $x$ from the central maximum is $x = L \tan \theta \approx L \sin \theta$ for small angles, where $L = 1 \text{ m}$. Calculating gives $x \approx 0.309 \text{ nm}$.

Light from a Laser Strikes a Diffraction Grating That Has