Question

Light with a wavelength of about 490 nm is made to pass through a diffraction grating. The angle formed between the path of the incident light and the diffracted light is 9.2° and forms a first-order bright band.

What is the number of lines per mm in the diffraction grating?
I really don't know how to do this!

Answer 1

It is 326 lines per mm

Answer 2

326.8 lines/mm

Step-by-step explanation:

The formula for the diffraction is:

`d sin \theta = n \lambda`

where we have

d is the grating spacing

`\theta = 9.2^(\circ)` is the diffraction angle

n = 1 (because we are reffering to the first-order maximum)

`\lambda=490 nm = 4.9\cdot 10^(-7) m` is the light wavelength

Re-arranging the equation, we can calculate the grating spacing d:

`d=(n \lambda)/(sin \theta)=((1)(4.9\cdot 10^(-7)m))/(sin 9.2^(\circ))=3.06\cdot 10^(-6) m=3.06\cdot 10^(-3)mm`

This is the distance between the lines in the diffraction grating: therefore, the number of lines per mm will be

`N=(1)/(d)=(1)/(3.06\cdot 10^(-3)mm)=326.8 mm^(-1)`