Chapter 47: Problem 13

Question: A grating has $315~{\rm rulings/mm}$. For what wavelngths in the visible spectrum can fifth order diffraction be observed?

Solution: Given the information we know that the distance between adjacent slits is

$$d~=~{1\over 315}~=~3.17\times 10^{-6}~{\rm m}$$

The location of the maximum interference fringe is at $\sin\theta~=~1$. Given, $d~=~5 \lambda$ for the fifth interference fringe at $\sin\theta~=~1$, means that $\lambda\le 635~{\rm nm}$ (and also $\lambda\ge 400~{\rm nm}$ for visible light).