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.