A diffraction grating has 5000 lines per cm If blue light wi

A diffraction grating has 5000 lines per cm. If blue light with a wavelength of 440 nm is used, what is the slit width? At what angles will the first and second order spectra be observed for this color?

Solution

given

5000 lines/cm

lamda = 440 nm

slit width, d = 1 cm/5000

= 0.01 m/5000

= 2*10^-6 m <<<<------------Answer

for first order, d*sin(theta1) = lamda

sin(theta1) = lamda/d

theta1 = sin^-1(lamda/d)

= sin^-1(440*10^-9/2*10^-6)

= 12.71 degrees <<<<------------Answer

for second order, d*sin(theta2) = 2*lamda

sin(theta2) = 2*lamda/d

theta2 = sin^-1(2*lamda/d)

= sin^-1(2*440*10^-9/2*10^-6)

= 26.1 degrees <<<<------------Answer