Question

What is the approximate wavelength of a light whose first-order bright band forms a diffraction angle of 45.0° when it passes

Answer 1

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

Ans: The wavelength is =  λ = 1414.21 nm

Explanation:
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