The spacing of ruled lines on a diffraction grating is 1770 nm.The grating is illuminated at normal incidence with a parallel beam of white light in the 400 nm to 700 nm wavelength band.The longest wavelength that appears in the third order spectrum is closest to:
A)590 nm
B)570 nm
C)550 nm
D)530 nm
E)610 nm

Question

Quizplus · Accepted Answer

The diffraction grating equation is d*sin(θ) = m*λ, where d is the spacing, m is the order, and λ is the wavelength. For the third order (m=3), the longest wavelength λ is when sin(θ) is maximum (i.e., 1). So, λ = d/m = 1770 nm / 3 = 590 nm.

The Spacing of Ruled Lines on a Diffraction Grating Is