So, what types of RF are these cases intended to block? If they block the frequency being used by the phone than if the blocking is complete the phone won’t work. If it’s partial than, as noted by the FCC and related in the article, the phone may attempt to compensate for the weakened signal by increasing it’s signal strength, thereby emitting higher levels of radiation itself, and reducing battery life in the process.

The Specific Absorption Rate test uses sophisticated instruments to measure the amount of radiation absorbed into the body, usually the head. At present, the generally recognized limit for absorbed electromagnetic energy is 1.6 watts per kilogram. All cell phones sold must be tested and have their compliance with this standard certified by their manufacturer. The electromagnetic fields from a cell phone depend upon the design of the cell phone and its antenna,how it operates, as well as how it is held and used. Tests conducted by the ABC show 20/20 has found that some of the country’s most popular cell phones can – depending on how they’re held – exceed the radiation limit. A cell phone’s antenna radiates in all directions. The health concern is about the radiation actually absorbed into the head, which is where cell phones are usually held. SAR tests conducted on the SAR Shield show that the product reduces SAR radiation by as much as 89%.

The papers found that, in male rats, there was “clear evidence” that exposure to cell phone radiation increased risk for a rare type of malignant tumor called schwannoma in the connective tissues that surround nerves in the heart (they found “equivocal” evidence for the same thing in female rats). They also found “some evidence” that the radiation caused malignant glioma—a type of brain cancer affecting glial cells—in the male rats.

In addition to the increased brain cancer risk, in male rats there was also “clear evidence” of a link between the radiation and malignant heart tumors and “some evidence” of a link to adrenal-gland tumors, according to the release. In mice and in female rats, however, the link between radiation and tumors was “equivocal,” or uncertain. The hierarchy, from most to least certain, of characterizations used by the NTP is: “clear evidence”; “some evidence”; “equivocal evidence”; and “no evidence.”Today’s cellphones use higher-frequency radiation that is less able to penetrate animal tissues than the radiation used in the study, the Times reports. Further, since cellphones became popular, epidemiologists have not observed an overall increase in the frequency of brain cancers known as gliomas in humans. 
The energy of electromagnetic radiation is determined by its frequency; ionizing radiation is high frequency, and therefore high energy, whereas non-ionizing radiation is low frequency, and therefore low energy. The NCI fact sheet Electromagnetic Fields and Cancer lists sources of radiofrequency radiation. More information about ionizing radiation can be found on the Radiation page.
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