Suppose you wanted to use a non-reflecting layer for radar waves to make an aircraft invisible. What would the thickness of the layer be to avoid reflecting 2 cm radar waves. (You can neglect changes of wavelength in the layer for this problem.) Would there be any problems as the aircraft turn

the thickness of the film for destructive interference is 1 cm

Explanation:

We can assume that the radar wave penetrates the layer and is reflected in the inner part of it, giving rise to an interference phenomenon of the two reflected rays, we must be careful that the ray has a phase change when

* the wave passes from the air to the film with a higher refractive index

* the wavelength inside the film changes by the refractive index

         λ = λ₀ / n

so the ratio for destructive interference is

            2 n t = m λ

            t = m λ / 2n

indicate that the wavelength λ = 2 cm, suppose that the interference occurs for m = 1, therefore it is thickness

            t = 1 2/2 n

            t = 1 / n

where n is the index of refraction of the anti-reflective layer. As they tell us not to take into account the change in wavelength when penetrating the film n = 1

            t = 1 cm

So the thickness of the film for destructive interference is 1 cm