Question

A diffraction grating with 230 lines per mm is used in an experiment to study the visible spectrum of a gas discharge tube. At what angle from the beam axis will the first order peak occur if the tube emits light with wavelength of 421.2 nm?

At what angle will the second order peak occur?

Solution)

We know,

d sin theta= wavelength

d = 1/230 per mm = 0.0043 mm X (10^6nm/mm) = 4347.82 nm

theta = first peak = arc sin (wavelength/d)

= 5.55 degrees

Now,

second peak = arc sin (2 *wavelength/d)

= 11.17 degrees

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