Diffraction Grating - Find Wavelength

Diffraction Grating- Find Wavelength

Question:

Light from an argon laser strikes a diffraction grating that has 5310 lines per centimeter. The central and first-order principal maxima are separated by 0.488 m on a wall 1.72 m from the grating. Determine the wavelength of the laser light in nm.

Answer:

The diffraction grating is a great number of single slits side by side. Each slit produces a diffraction pattern and these diffraction patterns interfere with one another resulting in very sharp bright peaks separated by broad dark bands. If the path difference for light from the slits is a whole wavelength the light from the slits will show constructive interference resulting in a bright peak. The condition for this constructive interference then is d*sin(q) = m*wavelength where d is the grating slit separation, m is an integer and q is the observation angle.

In the given problem d=1/5310cm=1.883e-4cm=1883nm. Sin(q)=.488/1.720=0.2837. The order, m, is 1 for the first order maxima. So we have wavelength=1833nm*0.2837=534.2nm.