A parallel beam of sodium light of wavelength 5.893×10^-7 m is incident normally on a diffraction grating. The angle between the two first-order spectra on either side of the normal is 28°. Find the number of ruling lines per mm on the grating.
1 Answer
Solution
Given,
Wavelength, \(\lambda=589.3mm=589.3\times10^{-9}\) m,
Angle (2θ) = 28° ⇒ θ = 14°
Number of lines per mm (N) = ?
We have,
d sin(θ) = λ (for the first order)
Or, \(\frac1N\sin\left(\theta\right)=\lambda\)
Or, \(N=\frac{\sin\left(\theta\right)}\lambda\)
Or, \(N=\frac{\sin\left(14\right)}{589.3\times10^{-9}}\)
Or, N = 410524.17 lines/m
∴ N = 410 lines/mm
Hence, the number of ruling lines per mm on the grating is 410 lines.
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