Question

A grating has 380 lines/mm. How many orders of the visible wavelength 457 nm can it produce in addition to the m = 0 order? Please explain your solution.

Answer 1

5 orders.

Step-by-step explanation:

The condition for diffraction maxima,

`sin \theta = mN\lambda\\m=(sin \theta)/(N\lambda)`

`m=(sin 90^(\circ))/((380(lines)/(mm)((1000mm)/(1m) )) 457* 10^(-9) m )\\m=5.75\simeq5`

So maximum m is 5 which means it produce 5 orders.

Therefore, the number of possible order will produce by visible light of wavelength 457 nm is 5 orders.