Figure 5 shows the arrangement used by Fizeau to determine the speed of light - AQA - A-Level Physics - Question 3 - 2022 - Paper 7

To determine if the speed of light can be calculated, we first calculate the maximum measurable speed using:

$v_{max} = n \cdot d \cdot t$

Where:

• $n = 720$ teeth
• $d = 8.5 \text{ km} = 8500 \text{ m}$
• The time $t$ for one rotation at 620 rev/min is:

$t = \frac{1 \text{ min}}{620 \text{ revolutions}} = \frac{60 \text{ s}}{620 \text{ rev}} \approx 0.09677 \text{ s/rev}$

The total time for 720 teeth equals:

$T = 720 imes 0.09677 \approx 69.69 \text{ s}$

So, the maximum possible speed of the light reflected can be approximated as:

$c = \frac{4 \cdot 8500 \cdot f_0}{69.69}$

Given that $c$ must be less than the speed of light in a vacuum, which is approximately $3 \times 10^8 \text{ m/s}$, this setup is unable to achieve that calculated speed under these conditions. Thus, the speed of light cannot be determined accurately.

$\epsilon_0$ is the electric field strength in free space, which relates to the charge density in electric fields, while $\mu_0$ is the magnetic field strength in free space, which relates to the magnetic flux density. Both constants are fundamental to understanding wave propagation, where $\epsilon_0$ characterizes the electric field component, and $\mu_0$ characterizes the magnetic field component, forming the basis of the relationship between electric and magnetic fields in electromagnetic waves.