Light from a laser strikes a diffraction grating.The central and first order principal maxima are separated by 0.325 m on a wall 1.00 m from the grating.Determine the distance separating adjacent slits in the grating if the wavelength of the laser light used is 454 nm.

Question

Quizplus · Accepted Answer

Using the diffraction grating formula $d \sin \theta = m \lambda$, where $d$ is the slit separation, $\theta$ is the angle of diffraction, $m$ is the order of the maximum, and $\lambda$ is the wavelength. For small angles, $\tan \theta \approx \sin \theta \approx \frac{x}{L}$, where $x$ is the separation of maxima on the screen and $L$ is the distance to the screen. For the first order maximum ($m=1$), $d = \frac{\lambda L}{x}$. Substituting $\lambda = 454 \times 10^{-9}$ m, $L = 1.00$ m, and $x = 0.325$ m, we find $d \approx 1470$ nm.

Light from a Laser Strikes a Diffraction Grating