Question

A pulse oxymeter determines a person’s oxygen saturation, that is what fraction of the hemoglobin in their bloodstream carries an oxygen molecule. Hemoglobin molecules that are carrying oxygen strongly absorb 940 nm waves, while hemoglobin without oxygen instead strongly absorbs 660 nm light. So, pulse oxymeters contain two light sources at 660 nm and 940 nm. Typically the device is (painlessly!) clipped onto person’s finger, and by comparing how much 660 nm and 940 nm light is transmitted through the finger, it can determine the oxygen saturation.

a) What type of electromagnetic waves are the 660 nm and 940 nm waves? Could you see either of them?

b) It turns out that the signals seen by an oxymeter vary with time due to one’s heartbeat. So typically each light is quickly pulsed on and off 30 times per second and the oxymeter looks at the peak values observed. In a pulse of light that lasts 1/30th of a second, how many 660 nm wavelengths are within the pulse?

c) What is the ratio of the speed of the 660 nm waves over the speed of the 940 nm waves? Explain.

Answer 1

(a) The 660 nm pule lies in the visible range ( specifically red) hence can be seen through naked eyes while 940 nm waves are infrared waves

(b) The frequency of the 660 nm wave is

Hence in one sec, there will be wavelength will be there so in 1/30th sec

number of wavelengths will be

(c) The ratio of the speed of the two waves will be equal unity in the air as both the wave will move with same speed which is the speed of light.

Although in the hemoglobin, it will be different. Let the frequency of two waves are . With the change in medium, the frequency of wave does not change although the speed and wavelength will change.

for vacuum or free space

In Haemoglobin,

Now by taking the ratio of velocity, we have