Unreasonable Results

To save money on making military aircraft invisible to radar, an inventor decides to coat them with a non-reflective material having an index of refraction of \({\rm{1}}{\rm{.20}}\), which is between that of air and the surface of the plane. This, he reasons, should be much cheaper than designing Stealth bombers.

(a) What thickness should the coating be to inhibit the reflection of \({\rm{4}}{\rm{.00 - cm}}\)wavelength radar?

(b) What is unreasonable about this result?

(c) Which assumptions are unreasonable or inconsistent?

Wavelength: The distance between identical points (adjacent crests) in adjacent cycles of a waveform signal propagated in space or along a wire is defined as the wavelength. This length is typically specified in wireless systems in metres (m), centimeters (cm), or millimeters (mm) .

(a) Considering the given information,

Redfractive index of film coating,\(n = 1.20\)

Wavelength of the radar,\(\lambda = 4\;cm\)

Apply the formula,

The formula calculates the thickness of the film producing destructive interference :

\(2t = \dfrac{\lambda }{{4n}}\)

Here,

The wavelength of the reflected light is denoted by\({\rm{\lambda }}\).

The redfractive index is n.

The t denotes the thickness of the film causing interference.

The thickness of the coating to prevent reflection is calculated as:

\(t = \dfrac{\lambda }{{4n}}\)

Putting the values,

\(\begin{aligned}t &= \dfrac{4}{{4 \times 1.2}}\\ &= 0.83\;\,cm\end{aligned}\)

Therefore, the requiredthickness of the coating to inhibit the reflection is\({\rm{0}}{\rm{.83\;cm}}\).

(b) The thickness of the film is extremely thick, resulting in a significant increase in the weight of the aircraft. Furthermore, as the area increases, the drag force increases dramatically.

Therefore, the requiredthickness of the film is very high.

(c) It is illogical to believe that any thickness of coating can be applied to an aircraft screen, because the thickness of the film is extremely thick, increasing the weight of the aircraft significantly. Furthermore, as the area increases, the drag force increases dramatically.

Therefore, it is unreasonable to think that the coating of any thickness can be applied on the aircraft screen.