Question

A physics instructor wants to project a spectrum of visible light colors from 400nm to 700nm as part of a classroom demonstration. She shines a beam of white light through a diffraction grating that has 500 lines per mm, projecting a pattern on a screen 2.4 m behind the grating.

a) how wide is the spectrum the corresponds to m=1?

b. How much distance separates the end of the m=1 spectrum and the start of m= 2 spectrum?

Answer 1

Answer:

a) 0.407 m

b) 0.1504 m

Explanation:

see attached picture.

Answer 2

(a) The  width of the spectrum that corresponds to m = 1 is determined as 0.41 m.

(b) The distance that separates the end of the m=1 spectrum and the start of m= 2 spectrum is 0.15 m.

Width of the spectrum

The width of the spectrum is calculated as follows;

d = (0.001)/500 = 2 x 10⁻⁶

dsinθ = mλ

for 400 nm

(2 x 10⁻⁶)sinθ = (1)(400 x 10⁻⁹)

θ = 11.54⁰

For 700 nm

(2 x 10⁻⁶)sinθ = (1)(700 x 10⁻⁹)

θ = 20.49⁰

Width of spectrum = Δy

Δy = 2.4tan(20.49) - 2.4tan(11.54) = 0.41 m

For m = 2

(2 x 10⁻⁶)sinθ = (2)(400 x 10⁻⁹)

θ = 23.58⁰

Width of spectrum from end of m = 1 and start of m = 2

Δy' =   2.4tan(23.58)  - 2.4tan(20.49)  = 0.15 m

Learn more about diffraction here: https://brainly.com/question/16749356

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