the width of the first-order rainbow on a screen 2.0 m behind the grating is Δy=0.431m
Finding the angle from a diffraction grating with split space d is necessary to get the fringe location ym.
dSinα=mλ
Slit spacing for a grating with N slits or lines per mm is
d=1/N
d=(1/600mm)
d=1.67×10⁻³mm
At a wavelength of 400 nm:
α=Sin⁻¹(mλ/d)
α=13.9°
The first order lowest wavelength fringe is located in the following location on the screen:
y1= Ltanα
y1=.49445m
For 700nm wavelength:
α=Sin⁻¹(mλ/d)
α=24.8°
The first order highest wavelength fringe is located in the following location on the screen:
y2= Ltanα
y2= .99255m
The first order lowest and highest wavelength fringe's difference is
Δy=(0.925595 - 0.49445)m
Δy=0.431m
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