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

explanation:

could i give you a exaplo that could you?

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.