Two spectral lines of wavelengths $590,\text{nm}$ and $594,\text{nm}$ are to be resolved using the fifth order ($m=5$) spectrum of a diffraction grating whose line spacing is $0.9,\mu \text{m}$. Using Rayleigh’s criterion, what is the minimum total number of illuminated slits $N$ required?

Step-by-step solution

1. Average wavelength $lambdaapprox(590+594)/2=592,\text{nm}$.
2. Resolution condition: $Deltalambda=\frac{\lambda }{mN}$. Here $Deltalambda=594-590=4,\text{nm}$.
3. Solve for $N$: $N=\frac{\lambda }{mDeltalambda}=\frac{592}{5\times 4}=29.6$.
4. Since $N$ must be an integer, round up to $30$.
5. Thus at least 30 illuminated slits are needed to resolve the two lines.

Concept tested: Grating resolving power

Published 13 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked