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

Answer:

5 orders.

Explanation:

The  condition for diffraction maxima,

$sin \theta = mN\lambda\\m=\frac{sin \theta}{N\lambda}$

$m=\frac{sin 90^{\circ}}{(380\frac{lines}{mm}(\frac{1000mm}{1m} )) 457\times 10^{-9} m }\\m=5.75\simeq5$

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.