A student used a laser pointer to direct monochromatic light normal to the plane of a diffraction grating as shown - Edexcel - A-Level Physics - Question 1 - 2023 - Paper 3

To determine if the spacing of the diffraction pattern is consistent, we can use the formula:

$d = \frac{n \lambda D}{x}$

Where:

• $d$ is the spacing of the grating,
• $n$ is the order of the maximum (first order maximum, so $n=1$),
• $\lambda$ is the wavelength of the light ($520nm = 520 \times 10^{-9} m$),
• $D$ is the distance from the grating to the screen ($2.75m$),
• $x$ is the distance from the central maximum to the first order maximum ($43.5cm = 0.435m$).

Plugging in the values:

$d = \frac{1 \times (520 \times 10^{-9}) \times 2.75}{0.435}$

Calculating:

$d = \frac{1.430 \times 10^{-6}}{0.435} = 3.29 \times 10^{-6} m = 3.29 \mu m$

The grating has 300 lines per mm, which means the spacing is:

$d_{grating} = \frac{1}{300 \times 10^3} = 3.33 \times 10^{-6} m = 3.33 \mu m$

Since $3.29 \mu m$ is approximately equal to $3.33 \mu m$, the spacing of the diffraction pattern is consistent with the given values.