Considering the Earth's atmosphere as a lens is quite an innovative idea. However, determining its diameter and focal length requires some creative thinking.

The diameter of the atmospheric lens would roughly correspond to the diameter of the Earth itself, which is approximately *12,742 kilometers (7,918 miles)*.

As for the focal length, it's challenging to provide a precise value since the atmosphere isn't a traditional lens with a fixed focal point. Nevertheless, we can consider the scale height of the atmosphere, which is the distance over which the atmospheric pressure decreases by a factor of e (approximately 2.718). The scale height of the Earth's atmosphere is around 8.5 kilometers (5.3 miles). This value doesn't directly translate to a focal length, but it gives an idea of the atmospheric layer's thickness.

To estimate the focal length of the atmospheric lens, we'd need more specific information about the atmospheric conditions and the wavelengths of interest. The atmosphere's refractive properties vary with temperature, pressure, and composition, making it difficult to pinpoint a precise focal length.

If we draw parallels with optical systems, the focal length of a lens is typically determined by its curvature and refractive index. Given the complexity of the Earth's atmosphere, calculating its focal length would require sophisticated modeling and simulation.

In certain scientific contexts, researchers have studied the atmospheric lensing effect, particularly in radio astronomy and gravitational lensing. However, these studies often focus on specific phenomena or wavelengths, and the results might not be directly applicable to a general atmospheric lens