Answer:
Here, the wavelength of the light λ, that has a its 2nd order maximum m=2, at θ = 45.0º, when falling on a grating with 5000 lines per centimeter, can be calculated using the principle of diffraction grating which states that:
[tex]dsinθ={m}{λ}[/tex] (See the attached illustration picture)
Explanation:
Where;
d=distance between lines = [tex]\frac{1cm}{5000}[/tex] (Given in the question)
m = order of the maximum = 2
θ=angle of diffraction of the light = 45.0º
and
λ = wavelength of the light = Unknown?
Now, we can do the calculation as follows,
[tex]\frac{sin45.0º}{5000}={2}{λ}[/tex]
[tex]{1.414x10^{-4}}={2}{λ}[/tex]
[tex]{λ}=\frac{1.414x10^{-4}}{2}[/tex]
[tex]{λ}={7.07x10^{-5}}[/tex]
Hence, the wavelength of light that has its second-order maximum at 45.0º when falling on a diffraction grating that has 5000 lines per centimeter is 0.0000707cm
