Answer to Question #202101 in Optics for Prachi

Question

6 principal maxima are observed in the diffraction pattern due to a diffraction grating. Calculate the number of lines per cm in the grating if the wavelength of the light is 5000 Å.

Answer 1

$(a+b)sinθ=nλ \\ N=\frac{1}{a+b} \\ θ=90° \\ (a+b)= nλ \\ (a+b) = 6 \times 5 \times 10^{-10} \\ = 3 \times 10^{-9} \\ N= \frac{1}{3 \times 10^{-9}}=3.33 \times 10^8 \;lines \; per \;m \\ = 3.33 \times 10^{10}\;lines \;per\;cm$