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Assuming that the limits of the visible spectrum are approximately 380 and 700 nm, find the angular range of the first-order visible spectrum produced by a plane grating that has 900 grooves/mm with the light incident normally on the grating.

Respuesta :

Answer:

angular range is ( 0.681 rad , 0.35 rad )

Explanation:

given data

wavelength λ = 380 nm = 380 × [tex]10^{-9}[/tex] m

wavelength λ  = 700 nm =  700 × [tex]10^{-9}[/tex] m

to find out

angular range of the first-order

solution

we will apply here slit experiment equation that is

d sinθ = m λ    ...........1

here m is 1 for single slit and d is = [tex]\frac{1}{900*10^3 m}[/tex]

so put here value in equation 1 for 380 nm

we get

d sinθ = m λ

[tex]\frac{1}{900*10^3}[/tex] sinθ = 1 × 380 × [tex]10^{-9}[/tex]

θ = 0.35 rad

and for 700 nm

we get

d sinθ = m λ

[tex]\frac{1}{900*10^3}[/tex] sinθ = 1 × 700 × [tex]10^{-9}[/tex]

θ = 0.681 rad

so angular range is ( 0.681 rad , 0.35 rad )

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