What is the approximate wavelength of a light whose first-order bright band forms a diffraction angle of 45. 0° when it passes through a diffraction grating that has 500. 0 lines per mm?.

** Missing info: Lines per mm = 500 **

The wavelength is =  λ = 1414.21 nm

Solution:

The formula for diffraction grading is:

dsinθ = mλ --- (1)

Where

d = 1/lines-per-meter = (1/500)*10^-3 = 2 * 10^-6

m = order = 1

λ = wavelength

θ = 45°

Plug in the values in (1):

(1) => 2*10^-6*sin(45°) = (1)λ

=> λ = 1414.21 nm

1414.21 nm

Explanation:

diffraction grating equation is

d sin θ = nλ

were looking for λ

d is the distance between the slits = 1/500 mm = .002 mm = 2000 nm

θ is diffraction angle = 45

λ is the wavelength of the light (what were looking for)

n is the order of diffraction = "first-order bright band" = 1

λ = wavelength

θ = 45°

Plug in

2000sin(45°) = (1)λ

=> λ = 1414.21 nm

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