Waves from two coherent sources, S₁ and S₂, produce an interference pattern - Scottish Highers Physics - Question 13 - 2018

To find the wavelength, we can rearrange the equation as follows:

$\lambda = \frac{S_{1}P - S_{2}P}{n}$

Given we need to find possible values of $\lambda$, we will consider different values of $n$. Since the path difference is given as 154 mm, we will test each option for the integer $n$.

1. For $n=1$: $\lambda = \frac{154 \text{ mm}}{1} = 154 \text{ mm}$. (not an option)
2. For $n=2$: $\lambda = \frac{154 \text{ mm}}{2} = 77 \text{ mm}$. (not an option)
3. For $n=3$: $\lambda = \frac{154 \text{ mm}}{3} \approx 51.33 \text{ mm}$. (not an option)
4. For $n=4$: $\lambda = \frac{154 \text{ mm}}{4} = 38.5 \text{ mm}$. (not an option)
5. For $n=5$: $\lambda = \frac{154 \text{ mm}}{5} = 30.8 \text{ mm}$, which corresponds to option D.

Based on our calculations and analysis, the wavelength of the waves is therefore approximately:

D. 30-8 mm.