Oxygenated hemoglobin absorbs weakly in the red (hence its red color) and strong

Question

Oxygenated hemoglobin absorbs weakly in the red (hence its red color) and strongly in the near infrared, whereas deoxygenated hemoglobin has the opposite absorption. This fact is used in a "pulse oximeter" to measure oxygen saturation in arterial blood. The device clips onto the end of a person's finger and has two light-emitting diodes --a red (675 nm) and an infrared (930 nm)-- and a photocell that detects the amount of light transmitted through the finger at each wavelength.

(a) Determine the frequency of each of these light sources.

(b) If 63% of the energy of the red source is absorbed in the blood, by what factor does the amplitude of the electromagnetic wave change? [Hint: The intensity of the wave is equal to the average power per unit area as given by the equation given below.]

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Explanation / Answer

we know, the relation, c = lamda*f (c is light speed, lamda is wavelength and f is frequency)

a) f_red = c/lamda_red

= 3*10^8/(675*10^-9)

= 4.44*10^14 Hz

f_infrared = c/lamda_infrared

= 3*10^8/(930*10^-9)

= 3.22*10^14 Hz

b) remaining energy of the wave = 0.37% of oroginal energy

so, I2 = 0.37*I1

From the given equation we can write,

Emax2^2/Emax1^2 = I2/I1

Emax2^2/Emax1^2 = = 0.37*I2/I1

Emax2/Emax1 = sqrt(0.37)

= 0.608

Emax2 = 0.608*Emax1

= 60.8% of Emax1

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