Question

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.

Answer 1

angular range is ( 0.681 rad , 0.35 rad )

Step-by-step explanation:

given data

wavelength λ = 380 nm = 380 ×
`10^(-9)` m

wavelength λ = 700 nm = 700 ×
`10^(-9)` 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 =
`(1)/(900*10^3 m)`

so put here value in equation 1 for 380 nm

we get

d sinθ = m λ

`(1)/(900*10^3)` sinθ = 1 × 380 ×
`10^(-9)`

θ = 0.35 rad

and for 700 nm

we get

d sinθ = m λ

`(1)/(900*10^3)` sinθ = 1 × 700 ×
`10^(-9)`

θ = 0.681 rad

so angular range is ( 0.681 rad , 0.35 rad )