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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Physics

Amani Cherry

7 March, 12:03

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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Dana Morrison · 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 °