The minimum thickness of the dielectric coating for a 2.78 cm radar wavelength, accounting for a π phase shift on reflection, is calculated to be 1.20 cm to achieve destructive interference.
To find the minimum desired thickness of the dielectric coating that inhibits radar reflection, we use the principle of destructive interference in thin films. The additional path length within the dielectric medium for the reflected wave is twice the thickness of the coating, and for destructive interference, this should equal an odd multiple of half the wavelength in the medium.
Given that the radar's wavelength (λ) is 2.78 cm in air and the index of refraction (n) of the dielectric is 1.16, we can find the wavelength of the radar inside the material by dividing the wavelength in air by the index of refraction, so λ' = λ / n. With the aircraft surface inducing a π phase shift, equivalent to half a wavelength, we need an additional λ' / 2 path within the dielectric for destructive interference. This results in a total path difference of (2t + λ' / 2), where t is the coating thickness. To satisfy constructive interference for the first minimum, this path difference should be an odd multiple of λ' / 2.
Calculating for the first minimum (i.e., the smallest thickness), we set (2t + λ' / 2) equal to λ' / 2. Solving for t yields:
t = (λ' / 2 - λ' / 2) / 2 = 0
However, due to the π (half-wavelength) phase shift upon reflection at the aircraft surface, we seek the second minimum:
t = (3λ' / 2 - λ' / 2) / 2 = λ' / 2
Substituting λ' and solving gives us:
t = (2.78 cm / (2 × 1.16)) = 1.20 cm
Therefore, the minimum thickness of the dielectric coating to achieve destructive interference for a 2.78 cm radar wavelength would be 1.20 cm.