1.1. A group of students are conducting an experiment to determine the wavelength of monochromatic light from a laser.

Fig. 24.1 shows the laser beam incident normally at a diffraction grating.

Fig. 24.1

The students use a diffraction grating with 600 lines mm⁻¹.

They vary the distance $x$ between the grating and the screen from 1.000 m to 2.000 m. They measure the distance $y$ from the central maximum to the second order maximum.

The students decide to plot a graph of $y$ against $\sqrt{{x}^{2}+{y}^{2}}$.

Show that the gradient of the graph is equal to sin θ, where θ is the angle between the central maximum and the second order maximum.

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1.2. Fig. 24.2 shows the graph plotted by the students.

Fig. 24.2

i) Use Fig. 24.2 to determine an accurate value of the wavelength λ of the light from the laser.

λ = ..................................................... m [3]

ii) Suggest why there are no error bars shown in Fig. 24.2.

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iii) Suggest how the precision of this experiment may be affected by using a protractor to measure the angle θ.

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