A diffraction grating is to be used to find the wavelength of the emission spectrum of a gas. The grating spacing is not known, but light of a known wavelength of 632.8 nm is deflected by 43.2° in the second order by this grating. Light of the wavelength to be measured is deflected by 34.9° in the second order. What is the wavelength of the light that is to be measured?

528.9 nm

Explanation:

For a grating dsinθ = mλ where m = order of grating, d = grating space, λ = wavelength of light and θ = angle of deflection of light

First, we find the grating space d = mλ/sinθ where m = 2 for second order, λ = 632.8 nm = 632.8 * 10⁻⁹ m, θ = 43.2°

d = mλ/sinθ = 2 * 632.8 * 10⁻⁹ m : sin43.2° = 1.849 * 10⁻⁶ m = 1.849 μm

We now find the wavelength of the light to be measured from λ = dsinθ/m

Here, θ = 34.9° and m = 2 for second order. So, we have

λ = dsinθ/m = 1.849 * 10⁻⁶ m * sin34.9° : 2 = 0.5289 * 10⁻⁶ m = 528.9 nm