In the first-order spectrum, maxima for two different wavelengths are separated on the screen by 3.40 mm. what is the difference between these wavelengths?

The solution would be like this for this specific problem:

Given:

diffraction grating slits = 900 slits per centimeter

interference pattern that is observed on a screen from the grating = 2.38m

maxima for two different wavelengths = 3.40mm

slit separation ... d = 1/900cm = 1.11^-3cm = 1.111^-5 m

Whenas n = 1, maxima (grating equation) sinθ = λ/d

Grant distance of each maxima from centre = y ...

As sinθ ≈ y/D y/D = λ/d λ = yd / D

∆λ = (λ2 - λ1) = y2. d/D - y1. d/D

∆λ = (d/D) [y2 - y1]

∆λ = 1.111^-5m x [3.40^-3m] / 2.38m ... ►∆λ = 1.587^-8 m