Yes, there is a direct formula that relates the amplitude of an electromagnetic wave to its intensity. In the context of electromagnetic waves, the intensity represents the power per unit area carried by the wave.
The formula connecting the amplitude (A) of an electromagnetic wave and its intensity (I) is:
I = (c * ε₀/2) * A²
Where: I is the intensity of the wave, A is the amplitude of the wave, c is the speed of light in a vacuum (approximately 3.00 x 10^8 meters per second), ε₀ is the vacuum permittivity (approximately 8.85 x 10^-12 farads per meter).
In this formula, the intensity (I) is directly proportional to the square of the amplitude (A) of the wave. This means that if you double the amplitude of the wave, the intensity will increase by a factor of four (2² = 4). Similarly, if you triple the amplitude, the intensity will increase by a factor of nine (3² = 9), and so on.
It's important to note that the formula assumes the wave is in a vacuum or free space, and it may vary slightly when considering different mediums or the presence of other factors.