Light from an argon laser of wavelength 449 nm strikes a diffraction grating.The central and first order principal maxima are separated by 0.550 m on a wall 2.00 m from the grating.Determine the number of grooves per centimeter for the diffraction grating.

Question

Quizplus · Accepted Answer

The separation of the maxima on the wall can be used to find the angle $\theta$ for the first order maximum using the tangent function, $\tan(\theta) = \frac{y}{L}$, where $y = 0.550 \, \text{m}$ is the separation and $L = 2.00 \, \text{m}$ is the distance to the wall. Solving for $\theta$ gives a small angle, allowing us to use the small angle approximation, $\tan(\theta) \approx \sin(\theta) \approx \theta$. The diffraction grating equation is $d\sin(\theta) = m\lambda$, where $d$ is the distance between grooves, $m = 1$ for the first order maximum, and $\lambda = 449 \, \text{nm} = 449 \times 10^{-9} \, \text{m}$ is the wavelength of the light. Rearranging for $d$ and converting to grooves per centimeter ($\text{cm}^{-1}$) gives the correct answer.

Light from an Argon Laser of Wavelength 449 Nm Strikes