Answer to Question #164090 in Optics for Haddensen

Question #164090


            A grating has 600 lines per mm and is illuminated norn1ally by light of wavelength 590nm.

            (a.) Find the direction of the first-order diffraction image.

            (b.) Is it possible to obtain a third-order image with this diffraction grating for this wavelength?

            (c.) What would be the effect on the number of orders, if the wavelength of the wave is increased?



1
Expert's answer
2021-02-22T10:27:08-0500

Given,

Diffraction granting=600 lines per mm

wavelength of light = 590nm

We know that, dsinθm=mλd\sin\theta_m = m\lambda

Here m = 1

sinθm=λd\Rightarrow \sin\theta_m=\frac{\lambda}{d}


sinθm=590×109m×6001×103\Rightarrow \sin\theta_m=\frac{590\times 10^{-9}m\times 600}{1\times 10^{-3}}


sinθm=354×103\Rightarrow \sin\theta_m=354\times 10^{-3}


sinθm=0.354\Rightarrow \sin\theta_m = 0.354

b) Yes, it can be obtained.

c) If wavelength of the wave get increase then the number of order will get decrease.


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