Question

A diffraction grating has 2000 lines per centimeter. at what angle will the first-order maximum be for 520-nm-wavelength green light?a diffraction grating has 2000 lines per centimeter. at what angle will the first-order maximum be for 520-nm-wavelength green light?

Answer 1

Applying diffraction equations;
d = 0.01/Number of lines; where 0.01 m = 1 cm, and d = spacing between lines

Therefore,
d = 0.01/2000 = 5*10^-6 m

Additionally,
d*Sin x = m*y; where x = Angle, m = order = 1, y = wavelength = 520 nm =520*10^-9 m

Substituting;
Sin x = my/d = (1*520*10^-9)/(5*10^-6) = 0.1040
x = Sin ^-1(0.104) = 5.97°

Therefore, first-order maximum for 520 nm will be 5.97°.