Question

You have a laser and want to estimate the wavelength. You decide to use a reflective diffraction grating to do this. The light is incident on the grating at 20 degrees with respect to normal. Using a grating with a groove distance of 5 mm, the first-order diffraction, is found at an angle of-12.5 degrees. Determine the wavelength of the source.

Answer 1

We can use Grating equation to calculate wavelength of light source. m$\lambda$ = d (sin$\theta$_i+ sin$\theta$_r) . Where m is order of diffraction, $\theta$_i is incident angle and $\theta$_r is diffracted angle.

m =1, $\theta$_i = 20°, $\theta$_r = -12.5° and d =5 mm = 5×10^-3m

1×$\lambda$ = 5×10^-3m ( sin20° + sin(-12.5°)) = 5×10^-3×0.125581m

$\lambda$ = 0.6279×10^-3m = 6.279×10^-4 m . (answer)