There's also radar reflection, "Observe that the received power drops with the fourth power of the range, so radar systems must cope with very large dynamic ranges in the receive signal processing." - https://www.eetimes.com/radar-basics-part-1/
I would also call it a classic as I learned it from this scene in Robert Heinlein's book "Rolling Stones": "The result was eight shiny right-angled corners facing among them in all possible directions —a radar reflector. ... The final result was to step up the effectiveness of radar from an inverse fourth-power law to an inverse square law — in theory, at least. In practice it would be somewhat less than perfectly efficient ...", https://archive.org/details/rollingstones0000robe_q7v9/page/...
A quick search on Google Scholar finds there's a fourth-power law for shock waves:
"A fourth-power law relating the stress jump through a steady structured shock wave and the maximum strain rate within the shock wave has received recognition as a unifying relation over a sensibly wide range of materials and shock compression amplitudes." - https://pubs.aip.org/aip/jap/article-abstract/107/1/013506/2...
"The third‐order nonlinear optical susceptibility χ(3) of this glass was found to be proportional to the fourth power of the radius of the colloid particles or the fourth power of the absorption coefficient at the peak of a plasmon band when the total volume of the colloid particles was constant."
There's also radar reflection, "Observe that the received power drops with the fourth power of the range, so radar systems must cope with very large dynamic ranges in the receive signal processing." - https://www.eetimes.com/radar-basics-part-1/
I would also call it a classic as I learned it from this scene in Robert Heinlein's book "Rolling Stones": "The result was eight shiny right-angled corners facing among them in all possible directions —a radar reflector. ... The final result was to step up the effectiveness of radar from an inverse fourth-power law to an inverse square law — in theory, at least. In practice it would be somewhat less than perfectly efficient ...", https://archive.org/details/rollingstones0000robe_q7v9/page/...
A quick search on Google Scholar finds there's a fourth-power law for shock waves:
"A fourth-power law relating the stress jump through a steady structured shock wave and the maximum strain rate within the shock wave has received recognition as a unifying relation over a sensibly wide range of materials and shock compression amplitudes." - https://pubs.aip.org/aip/jap/article-abstract/107/1/013506/2...
"Observations on the fourth-power scaling of high-pressure shock waves in solids" at https://pubs.aip.org/aip/jap/article-abstract/130/24/245901/...
and one with irradiance, though at the forth-power of the cosine:
"The cosine-fourth-power law states that the irradiance at any point in the image formed by a photographic lens, in the absence of vignetting, is equal to E_0 cos^4 β" - https://nvlpubs.nist.gov/nistpubs/jres/39/jresv39n3p213_A1b....
I also found the following at https://pubs.aip.org/aip/jap/article-abstract/75/6/3075/4001... :
"The third‐order nonlinear optical susceptibility χ(3) of this glass was found to be proportional to the fourth power of the radius of the colloid particles or the fourth power of the absorption coefficient at the peak of a plasmon band when the total volume of the colloid particles was constant."