Answer to Question #120408 in Optics for Dheeraj

Question

A grating of width 2cm is capable of resolving D1 and D2 lines of Sodium in the 3rd order. If the wavelength seperation of D1 and D2 lines is 6 Angstrom and average wavelenth of D1 and D2 lines is 5893 Angstrom. Then the number of lines on the grating?

Answer 1

The condition for maxima for D1 (5890 Angstrom) and D2 (5896 Angstrom):

$$d=m\lambda=3\cdot5893\cdot10^{-10}=1.768\cdot10^{-6}\text{ m}.$$

The number of lines is

$$N=x/d=\frac{0.02}{1.786\cdot10^{-10}}=11312.$$