Question

a nearly monochromatic beam of light with an average wavelength of 514 nm is incident normally on a diffraction grating 1.30 cm wide with 110 lines/cm. what is the smallest wavelength difference (in nm) this grating can resolve in the second order diffraction with this beam?

Answer 1

smallest wavelength difference (in nm) this grating can resolve in the second order diffraction with this beam is 8 degree

The formula for diffraction grating: Obviously, d = \frac {1} { N }, where N is the grating constant, and it is the number of lines per unit length. Also, n is the order of grating, which is a positive integer, representing the repetition of the spectrum so in this case the wavelength difference can be calculated as  514 nm/ 1.30 X 110 =3.59 X2 =approx 8.Wavelengths between 100 nm and 10 m correspond to the optical regime, where grating application is most prevalent. In that situation, the groove density can range from a few tens to a few thousand grooves per millimeter, similar to echelle gratings.

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