Question #102515
A grating has 10,000 lines per cm. Calculate the maximum number of principal maxima that can be formed for light of wavelength 487 nm.
1
Expert's answer
2020-02-10T09:44:22-0500

The distance between slits is 110000=104cm=106cm\dfrac{1}{10000}=10^{-4}cm=10^{-6}cm

Once a value for the diffraction grating’s slit spacing d has been determined, the angles for the sharp lines can be found using the equation

dsinθ=mλdsin\theta=m\lambda

where θ\theta is angle between normal and maximum direction; m is number of principal maxima;

λ=487nm is wavelength. Therefore

m=dsinθ/λm=dsin\theta/\lambda


Using the properties of sine function

sinθ1sinθ⪕1


Hence

mdλ=106487×109=2.053m⪕ ​ \dfrac{d }{\lambda} =\dfrac{10^{-6}}{487\times 10^{-9}}=2.053 ​


As result get the maximum number of principal maxima is equal to 2.



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