Final answer:
To eliminate the reflection of red light with a wavelength of 750 nm, a dielectric coating with a required dielectric constant of 2 and a minimum thickness of 93.75 nm needs to be applied to the glass. The percentage of reflected power for violet light with a wavelength of 420 nm can be calculated using the phase difference between the reflected and transmitted waves due to the coating.
Step-by-step explanation:
To eliminate the reflection of red light with a wavelength of 750 nm, a dielectric coating needs to be applied to the glass. The required dielectric constant can be found using the formula εr = (n^2)/(μr), where n is the index of refraction and μr is the magnetic permeability. In this case, since μr = 1, the dielectric constant would be εr = (n^2)/1 = n^2. Setting εr to 4, we find that the index of refraction n is √4 = 2. Therefore, the required dielectric constant is 2 and the minimum thickness of the coating can be found using the formula t = (λ)/(4n), where λ is the wavelength in air. Substituting the values, we get t = (750 nm)/(4 x 2) = 93.75 nm.
To calculate the percentage of incident power reflected for violet light with a wavelength of 420 nm, we need to determine the phase difference between the reflected and transmitted waves due to the coating. This can be done using the formula δ = (2πnt)/(λ), where δ is the phase difference, n is the index of refraction, t is the thickness of the coating, and λ is the wavelength in air. Substituting the values, we get δ = (2π x 2 x 93.75 nm)/(420 nm) ≈ 3.35 radians. From this, we can calculate the reflection coefficient using the formula R = (sinδ)^2. Finally, we can find the percentage of reflected power by multiplying R by 100.