the mathematical details underlying how their flash devices' guide number changes with different ISO sensitivities. Still, it can be helpful when comparing flash devices to understand how guide numbers vary with ISO sensitivity. Usually manufacturers state their products' guide number ratings relative to an ISO sensitivity of 100. However, some manufacturers of flash devices may provide guide numbers ratings specified relative to ISO 200, which increases its guide number by 41 percent relative to those given at ISO 100. The below table shows the proportional change in a flash device's guide number relative to both ISO 100 and ISO 200. Note that the extremely high guide numbers shown in the right-hand portion of the table have a limited real-world ability to extend flash distances. As the above photo illustrates, the fnumber × distance reciprocal relationship breaks down when on-camera flash devices that are set to full or near-full power are used in combination with cameras set to very high ISO sensitivities and large apertures (exceedingly long distances). ISO settings like 102,400 can yield guide numbers in excess of 1220 (m) / 4000 (ft) that seldom if ever permit extremely long-range flash photography due to particulates and aerosols typically present in outside air that fog images with haze glare and attenuate the reach of the light. Except in unusual atmospheric conditions, extraordinarily large guide numbers will produce suitable results only by either positioning the flash device off-axis from the camera by a fair distance or by shooting at the smallest apertures. Note B: The ISO sensitivities shown in this table are their common nomenclature values; their actual underlying values may be slightly different, such as ISO 250, which is actually approximately 252. Effect of filters Filters reduce guide numbers regardless of whether they are gels placed over the flash device or are lens filters on the camera. Flash devices may come with detachable color-correction gels or filters to match the color of the flash with different types of ambient lighting such as incandescent and fluorescent. Some modern flash devices can even detect when color-correction gels have been attached and automatically compensate for their effect on guide numbers. Unless a hot shoe-mounted electronic flash device's power can be controlled by a camera via through-the-lens metering (TTL), guide numbers must be manually compensated for the effect of on-lens filters. For instance a typical polarizing filter, which attenuates 1–1.5 fstops, will diminish guide numbers