A diffraction grating with 210 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 506.0 nm

Explanation:

Width of slit a = 1 x 10⁻³ / 210

a = 4.76 x 10⁻⁶ m .

angle at which first order peak is formed

= λ / a         (where λ is wavelength and a is width of slit)

given λ = 506 x 10⁻⁹ m

a = 4.76 x 10⁻⁶

θ = 506 x 10⁻⁹ / 4.76 x 10⁻⁶

= 106.3 x 10⁻³ radian .

first order peak is formed  at an angle of 106.3 x 10⁻³ radian .

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50 inches should be the resultant vector