Question

Calculate 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. Note: if there are 5,000 lines per cm, then the distance between lines (our value for d) is cm/5,000.

Answer 1

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:

`dsinθ={m}{λ}` (See the attached illustration picture)

Step-by-step explanation:

Where;

d=distance between lines =
`(1cm)/(5000)` (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,

`(sin45.0º)/(5000)={2}{λ}`

`{1.414x10^(-4)}={2}{λ}`

`{λ}=(1.414x10^(-4))/(2)`

`{λ}={7.07x10^(-5)}`

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