Suppose a light wave is in the visible spectrum, with frequency 740 THz(which will have a deep purple color). What will be the ratio of the electric to magnetic fields constitute the light wave? What fraction of the total energy is conveyed by the electric field?
To determine the ratio of the electric to magnetic fields of a light wave, we can use the equation for the strength of an electromagnetic wave:
c = λf
where:
c is the speed of light (approximately 3 x 10^8 m/s),
λ is the wavelength of the wave,
f is the frequency of the wave.
First, we need to find the wavelength of the light wave with a frequency of 740 THz. To do this, we rearrange the equation to solve for λ:
λ = c / f
λ = (3 x 10^8 m/s) / (740 x 10^12 Hz)
= 4.05 x 10^-7 m
Now that we have the wavelength, we can calculate the ratio of the electric (E) to magnetic (B) fields:
E/B = c
E/B = (3 x 10^8 m/s)
So, the ratio of the electric to magnetic fields constitutes the speed of light.
To find the fraction of total energy conveyed by the electric field, we use the equation:
Fraction of energy conveyed by E = (E^2) / (E^2 + B^2)
To simplify the calculation, we can consider that the ratio of the electric to magnetic fields is equal to 1:
E = B = (3 x 10^8 m/s)
Fraction of energy conveyed by E = ((3 x 10^8)^2) / (((3 x 10^8)^2) + ((3 x 10^8)^2))
= (9 x 10^16) / (18 x 10^16)
= 0.5
Therefore, the fraction of the total energy conveyed by the electric field is 0.5 or 50%.