A diffraction grating with 1000 lines per mm is used in a spectrometer to measure the wavelengths of light emitted from a gas discharge tube. You measure the diffraction angle to be at 20° for one emission line. What would happen to this emission line's diffraction angle if you replaced the diffraction grating with one having 500 lines per mm instead

Question

Yadiel Norman

Physics

13 February, 17:58

A diffraction grating with 1000 lines per mm is used in a spectrometer to measure the wavelengths of light emitted from a gas discharge tube. You measure the diffraction angle to be at 20° for one emission line. What would happen to this emission line's diffraction angle if you replaced the diffraction grating with one having 500 lines per mm instead

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Aurora Cameron · Answer 1

= 9.8°

Explanation:

Width of one slit (a₁) = 1 / 1000 mm=0.001 mm = 10⁻⁶ m.

width of one slit in case 2 (a₂) = 1/500 = 2 x 10⁻⁶ m

angular position of fringe, Sinθ = n λ / a

n is order of fringe, λ is wave length of light and a is slit aperture

So Sinθ ∝ 1 / a

Sin θ₁ / Sin θ₂ = a₂/a₁;

Sin20°/sinθ₂ = 2 / 1

sinθ₂ = Sin 20° / 2 =.342/2 =.171

θ₂ = 9.8 °