When light of wavelength 5.0 × 10⁻⁷ m is incident normally on a diffraction grating the fourth-order maximum is observed at an angle of 30° - AQA - A-Level Physics - Question 17 - 2017 - Paper 1

The order of the maximum is $m = 4$.

The angle for the fourth-order maximum is given as $θ = 30°$.

The diffraction grating equation is given by: $d imes ext{sin}(θ) = m imes λ$ Where $d$ is the grating spacing (distance between lines). Rearranging the equation to find $d$ gives: $d = \frac{m imes λ}{ ext{sin}(θ)}$ Substituting the values: $d = \frac{4 imes 5.0 imes 10^{-7}}{ ext{sin}(30°)}$

Since $\text{sin}(30°) = 0.5$, we can substitute this into the equation: $d = \frac{4 imes 5.0 imes 10^{-7}}{0.5} = 4.0 imes 10^{-6} ext{ m}$

The number of lines per mm (N) is given by: $N = \frac{1}{d} = \frac{1}{4.0 imes 10^{-6}}$ To convert this into lines per mm (1 m = 1000 mm): $N = \frac{1000}{4.0 imes 10^{-6}} = 2.5 imes 10^{5} ext{ lines/mm}$

The number of lines per mm on the diffraction grating is $2.5 imes 10^{5}$.