White light (380nm-750 nm) strikes a diffraction grating (900 lines/mm) at normal incidence. What is the highest-order visible maximum that is formed?

Highest order: m = 1

Explanation:

Formula for solving this is;

dsin θ_m = mλ

We want to find m, thus;

m = (dsin θ_m)/λ

We are told that White light spans from 380nm - 750 nm. Thus, at maximum, λ = 750 nm.

θ_m = 90°

d = (900 lines/mm) = 9000 × 10^(-7) lines/nm

Since we want to find m, the units nm has to cancel out in the equation.

Thus, we will write d in nm/lines as (10^(7))/9000 nm/lines

Thus;

m = ((10^(7))/9000 × sin 90)/750

m = 1.48

Approximately 1

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