Question

A grating has 470 lines/mm. how many orders of the visible wavelength 538 nm can it produce in addition to the m = 0 order?

Answer 1

Three complete orders on each side of the m=0 order can be produced in addition to the m = 0 order.

The ruling separation is

d=1 / (470mm −1) = 2.1×10⁻³ mm

Diffraction lines occur at angles θ such that dsinθ=mλ, where λ is the wavelength and m is an integer.

Notice that for a given order, the line associated with a long wavelength is produced at a greater angle than the line associated with a shorter wavelength.

We take λ to be the longest wavelength in the visible spectrum (538nm) and find the greatest integer value of m such that θ is less than 90°.

That is, find the greatest integer value of m for which mλ<d.

since  d / λ = 538×10⁻⁹m / 2.1×10 −6 m ≈ 3

that value is m=3.

There are three complete orders on each side of the m=0 order.

The second and third orders overlap.

Learn more about diffraction here : brainly.com/question/16749356

#SPJ4