Problems
275
The U.S. Food and Drug Administration limits the emission of microwave ovens
to no more than 5 mW/cm 2 beyond 5 cm from the oven surface.
Because the eyes have low blood circulation, they are the first tissue in the body
to be damaged by thermal heating due to microwaves. Cataracts occur for sustained
intensities above about 100 mW/cm 2 .
Microwaves of frequency 5.8 GHz with intensity of 30 mW/cm 2 , will cause an
increase of facial skin temperature by 0.48 ◦ C. With the same intensity, the corneal
surface of the eye heats by 0.7 ◦ C.
7.31.3 Cell Phone Radiation
Cell phones use frequencies in the 800 MHz and the 1900 MHz bands. At these
frequencies, the penetration depth of microwaves into biological tissue is less than
2 cm. Cell phones typically emit radio wave power of less than one watt, with
intensities typically less than 0.5 W/cm 2 near the phone. Due to wave reflection
and absorption in the skin and hypodermis surrounding the skull, brain exposure is
usually less than 1 mW/cm 2 .
Some attention has been given to the effects of cell phone radiation (with
frequencies in the GHz region) and the radiation of power lines (with frequency
of 60 Hz), since these radiations, although relatively weak, are pervasive and longterm.
Bluetooth devices transmit at frequencies about 2.4 and 2.5 GHz, but with far
less radiation energy than cell phones.
Problems
7.1 Laser light has been made with an intensity of 10 12 W/cm 2 . What is the energy
density in this light?
7.2 Two identical polarizing sheets are placed perpendicular to a light beam, but
one is rotated 23 ◦ relative to the first. If unpolarized light arrives at the first sheet,
what will be the percent loss in intensity of light after it passes through both sheets?
7.3 Most microwave ovens operate at a frequency of 2450 MHz. What is the
wavelength of this wave? How much energy (in electron-volts) does each such
microwave photon carry? Will such a photon cause atomic ionization?
7.4 The application of Stefan’s law to our skin includes radiation in the radio
end as well as the higher frequency end of the electromagnetic spectrum. Use
Planck’s expression for the intensity of light emission per unit frequency interval to
numerically estimate the percent of radiation that the skin emits just in the radio part
275
The U.S. Food and Drug Administration limits the emission of microwave ovens
to no more than 5 mW/cm 2 beyond 5 cm from the oven surface.
Because the eyes have low blood circulation, they are the first tissue in the body
to be damaged by thermal heating due to microwaves. Cataracts occur for sustained
intensities above about 100 mW/cm 2 .
Microwaves of frequency 5.8 GHz with intensity of 30 mW/cm 2 , will cause an
increase of facial skin temperature by 0.48 ◦ C. With the same intensity, the corneal
surface of the eye heats by 0.7 ◦ C.
7.31.3 Cell Phone Radiation
Cell phones use frequencies in the 800 MHz and the 1900 MHz bands. At these
frequencies, the penetration depth of microwaves into biological tissue is less than
2 cm. Cell phones typically emit radio wave power of less than one watt, with
intensities typically less than 0.5 W/cm 2 near the phone. Due to wave reflection
and absorption in the skin and hypodermis surrounding the skull, brain exposure is
usually less than 1 mW/cm 2 .
Some attention has been given to the effects of cell phone radiation (with
frequencies in the GHz region) and the radiation of power lines (with frequency
of 60 Hz), since these radiations, although relatively weak, are pervasive and longterm.
Bluetooth devices transmit at frequencies about 2.4 and 2.5 GHz, but with far
less radiation energy than cell phones.
Problems
7.1 Laser light has been made with an intensity of 10 12 W/cm 2 . What is the energy
density in this light?
7.2 Two identical polarizing sheets are placed perpendicular to a light beam, but
one is rotated 23 ◦ relative to the first. If unpolarized light arrives at the first sheet,
what will be the percent loss in intensity of light after it passes through both sheets?
7.3 Most microwave ovens operate at a frequency of 2450 MHz. What is the
wavelength of this wave? How much energy (in electron-volts) does each such
microwave photon carry? Will such a photon cause atomic ionization?
7.4 The application of Stefan’s law to our skin includes radiation in the radio
end as well as the higher frequency end of the electromagnetic spectrum. Use
Planck’s expression for the intensity of light emission per unit frequency interval to
numerically estimate the percent of radiation that the skin emits just in the radio part