Question

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

Answer 1

= 9.8°

Step-by-step 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 °