Monochromatic light of wavelength $500 \mathrm {~nm}$ is incident normally on a diffraction grating. If the third-order maximum of the diffraction pattern is observed at $32.0 ^ { \circ }$, what is the total number of maxima can be seen?

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Quizplus · Accepted Answer

The diffraction grating equation is $d \sin \theta = m \lambda$. For the maximum order $m$, $\sin \theta$ must be less than or equal to 1. Given $\lambda = 500 \, \text{nm}$, and using the third-order maximum at $32^\circ$, we find $d$. The maximum $m$ is when $\sin \theta = 1$, so $m = \frac{d}{\lambda}$. Calculating gives $m = 11$, meaning 11 maxima (orders 0 to 10) can be seen.

Monochromatic Light of Wavelength 500 nm500 \mathrm {~nm}500 nm Is Incident Normally on a Diffraction Grating

Monochromatic Light of Wavelength $500 \mathrm {~nm}$ Is Incident Normally on a Diffraction Grating