What is the maximum number of orders that can be observed using a plane grating ?

What is the maximum number of orders that can be observed using a plane grating of 300 lines/mm for normally incident light of wavelength 546 nm? If light of all wavelengths from 400 to 700 nm were used, what wavelengths would be superposed on the 546 nm wavelength in the highest of these orders?What is the maximum number of orders that can be observed using a plane grating ?The direction of the nth order principal maximum is given by



(a+b) sin 胃n = n位



a+b = 1 / 300 mm = 10^-3 / 300 m



To observe a principal maximum 胃 %26lt; 90 or sin 胃 %26lt; 1



For n = 1

sin 胃1 = 位 / (a+b) = 546x10^-9 x300 / 10^-3 = 0.1638

For n = 6, sin 胃6 = 0.1638 x 6 = 0.9828

For n = 7 , sin 胃7 = 0.1638 x 7 = 1.1466



So the maximum no. of orders visible is 6



The maximum possible orders for the wavelengths 400 nm and 700 nm is 8 and 4 respectively.



Find the values of the wave lengths in these orders that satisfy sin 胃 = 0.9828. These wave lengths will superimpose on the wave length 546 nm



0.9828 = 位1 x 300 x 8 x10^-6

位1 = 409.5 x10^-6 m = 409.5 nm

位2 = 0.9828/300x7 = 468 nm

位3 = 0.9828 /300x6 = 546 nm

位4 = 0.9828/300x5 = 655.2 nmWhat is the maximum number of orders that can be observed using a plane grating ?Use the diffraction equation.

nL = d.sin(theta[n])

sin(theta[n]) = nL/d (L is wavelength)

When theta[n] gets to 90 deg you won't see the spectrum.