Chapter 47: Problem 2

Question: A diffraction grating of width $w~=~2.86~{\rm cm}$ produces a deviation of $\theta_2~=~33.2^o$ in the second order with light of wavelength $\lambda~=~612~{\rm nm}$. Find the total number of rulings on the grating.

Solution: The second order maximum is in the angular location determined by $d\sin\theta_2~=~2\lambda$, and from the information given in the question, indicates that the distance between adjacent slits on the grating is $d~=~2.24\times 10^{-6}~{\rm m}$. Therefore, given the width of the grating, we know that $N~=~w/d~=~1.28\times 10^4$.