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3 years ago

13

A diffraction grating with 230 lines per mm is used in an experiment to study the visible spectrum of a gas discharge tube. At w

hat angle from the beam axis will the first order peak occur if the tube emits light with wavelength of 405.3 nm? Tries 0/20 At what angle will the second order peak occur?

1 answer:

mr_godi [17]3 years ago

6 0

Answer:

θ₁ = 5.4°

θ₂ = 10.86°

Explanation:

The angle ca be found by using grating equation:

mλ = d Sinθ

where,

m = order of diffraction

λ = wavelength = 405.3 nm = 4.053 x 10⁻⁷ m

d = grating element = 1/230 lines/mm = 0.0043 mm/line = 4.3 x 10⁻⁶ m/line

θ = angle = ?

FOR m = 1:

(1)(4.053 x 10⁻⁷ m) = (4.3 x 10⁻⁶ m/line) Sin θ₁

Sin θ₁ = 0.09425

θ₁ = Sin⁻¹(0.09425)

<u>θ₁ = 5.4°</u>

<u></u>

FOR m = 2:

(2)(4.053 x 10⁻⁷ m) = (4.3 x 10⁻⁶ m/line) Sin θ₁

Sin θ₂ = 0.1885

θ₂ = Sin⁻¹(0.1885)

<u>θ₂ = 10.86°</u>

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