Answer:
Δy=0.431m
Explanation:
Diffraction grating with split space d,to find the fringe position ym,we must to find the angle from
dSinα=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)
[tex]\alpha =Sin^{-1}(\frac{400*10^{-9} }{1.67*10^{-6}} )\\ \alpha =13.910^{o}[/tex]
And the position of first order lowest wavelength fringe on the screen is:
[tex]y_{1}=Ltan\alpha_{1}\\y_{1}=2tan(13.910)\\ y_{1}=0.49445m[/tex]
For 700nm wavelength:
α=Sin⁻¹(mλ/d)
[tex]\alpha =Sin^{-1}(\frac{700*10^{-9} }{1.67*10^{-6}} )\\ \alpha_{2} =24.83^{o}[/tex]
And the position of first order highest wavelength fringe on the screen is:
[tex]y_{2}=Ltan\alpha_{2}\\y_{2}=2tan(24.83)\\ y_{2}=0.925595m[/tex]
The difference between the first order lowest and highest wavelength fringe is
Δy=(0.925595 - 0.49445)m
Δy=0.431m
