The wavelengths of the visible spectrum are approximately 400nm (violet) to 700nm (red). Find the angular width of the first-order visible spectrum produced by a transmission diffraction grating with 405 lines per millimeter when white light falls normally on the grating.

Leypoldon 2022-08-07 Answered
The wavelengths of the visible spectrum are approximately 400nm (violet) to 700nm (red). Find the angular width of the first-order visible spectrum produced by a transmission diffraction grating with 405 lines per millimeter when white light falls normally on the grating. Give the answer in degrees.
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Answers (1)

Lisa Acevedo
Answered 2022-08-08 Author has 18 answers
As given thatgrating with 405 lines per millimeter
d = 1 405   l i n e   l m m
or
d = 1 405 × 10 3   l i n e   1 m d = 2.469 × 10 6   m
we know
d sin θ = n λ sin θ 1 = n λ d sin θ 1 = 1 × 400 × 10 9 2.469 × 10 6 θ 1 = 9.32
similarly
sin θ 2 = n λ d sin θ 2 = 1 × 700 × 10 9 2.469 × 10 6 θ 2 = 16.47
hence the angular width is
angular width=16.47-9.32
angular width= 7.15

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