Black Body Radiation (Edexcel A Level Physics): Exam Questions

An oximeter is a device used in hospitals to monitor the oxygen level in a patient’s blood.

In an oximeter, two light-emitting diodes (LEDs) are mounted opposite light sensors in a clip and attached to the patient’s finger. One of the LEDs produces red light and the other produces infrared.

The intensity $I$ of electromagnetic radiation received by the detector, after passing through a thickness $x$ of blood, is given by

$I=I_0{e}^{-\mu x}$

where $I_0$ is the intensity that would have been received if the blood were not present and $\mu$ is the attenuation coefficient of blood.

The red LED emits visible light of wavelength 650 nm and the infrared LED emits infrared of wavelength 950 nm.

The graph shows how $\mu$ varies with wavelength $\lambda$ for oxygenated blood and deoxygenated blood.

$I_0$for the infrared LED is 1.8 W m^–2. 

Calculate $I$ for the infrared after passing through 1.4 mm of oxygenated blood.

$I$ = .......................................................

The oximeter determines $I$/$I_0$ the fraction of radiation transmitted at each wavelength.

Deduce whether $I$/$I_0$ will be smaller for the red or the infrared radiation if the blood is deoxygenated.

It is suggested that ambient light could affect the readings produced by the oximeter.

Halogen lamps have a filament temperature of 3200 K.

Deduce whether the light from such a lamp would have a significant effect on the oximeter readings.

The cosmic microwave background (CMB) radiation is detected to come from all directions in space equally. The graph shows how the intensity of the CMB radiation varies with its wavelength.

Show that the graph is consistent with a black-body temperature of about $3\mathrm{K}$.