Will direct exposure to the Sun damage all digital cameras equally?

Considerations of optical damage induced by thermal effects were initiated by an apparent paradox: small and large diameter lenses with the same f-number produce an image of the Sun with the same irradiance. Thus, if one assumes that a damage threshold is given by irradiance (or intensity, as it is specified by most laser optics companies, in relation to continuous-wave lasers), all digital cameras should have the same probability of being damaged when pointed at the Sun. However, smartphones and in general small cameras are unaffected, while optical sensor arrays of larger cameras are often overheated and irreversibly damaged by the Sun. Therefore, the temperature rise responsible for the damage is not simply due to the irradiance of the Sun's image, but is actually related to lens size in a more subtle way. A simple thermal model shows that such a temperature rise is proportional to the linear power density (power/illuminated spot diameter) at focus. A web search shows that this important result is generally overlooked, although it is used by two renowned laser optics companies. This short article discusses the heating of an optical sensor as a practical example of applications of geometrical optics and heat transport laws at an undergraduate level.