The wavelength fringe is 0.431 m.
Diffraction grating with split space d, to find the fringe position ym, we must to find the angle from
d Sinα = mλ
A grating with N slits or lines per mm has slit spacing of
d = 1/N
d = (1/600mm)
d = 1.67×10⁻³mm
For 400nm wavelength:
α = Sin⁻¹(mλ/d)
α = Sin⁻¹(400*10⁻⁹/1.67*10⁻⁶)
α = 13.910°
And the position of first order lowest wavelength fringe on the screen is:
y₁ = L.tanα
y₁ = 2tan(13.910)
y₁ = 0.49445 m
For 700nm wavelength:
α = Sin⁻¹(mλ/d)
α = 24.83°
And the position of first order highest wavelength fringe on the screen is:
y₂ = L.tanα₂
y₂ = 0.925595 m
The difference between the first order lowest and highest wavelength fringe is
Δy = (0.925595 - 0.49445)m
Δy = 0.431m
Therefore, the wavelength fringe is 0.431 m.
To know more about wavelength, refer: https://brainly.com/question/28384782
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[NOTE: THIS IS AN INCOMPLETE QUESTION. THE COMPLETE QUESTION IS: White light (400–700 nm) is incident on a 600 line/mm diffraction grating. What is the wavelength of the first-order rainbow on a screen 2.0 m behind the grating?]
