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

Answer:

326.8 lines/mm

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:

$d=\frac{n \lambda}{sin \theta}=\frac{(1)(4.9\cdot 10^{-7}m)}{sin 9.2^{\circ}}=3.06\cdot 10^{-6} m=3.06\cdot 10^{-3}mm$

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

$N=\frac{1}{d}=\frac{1}{3.06\cdot 10^{-3}mm}=326.8 mm^{-1}$