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  • Estimating the following two numbers should be interesting. The first number will tell you why radio engineers do not need to worry much about photons! The second number tells you why our eye can never ‘count photons’, even in barely detectable light. (b)

Q: 11.25 (b) Estimating the following two numbers should be interesting. The first number will tell you why radio engineers do not need to worry much about photons! The second number tells you why our eye can never ‘count photons’, even in barely detectable light.The number of photons entering the pupil of our eye per second corresponding to the minimum intensity of white light that we humans can perceive (\sim10^-^1^0\hspace{1mm}Wm^2). Take the area of the pupil to be about 0.4 cm2, and the average frequency of white light to be about 6\times10^1^4\ Hz.

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The minimum perceivable intensity of white light(I)=10-10 Wm-2

Area of the pupil(A)=0.4 cm2=4\times10-5 m2

Power of light falling on our eyes at minimum perceivable intensity is P

P=IA

P=10-10\times4\times10-5

P=4\times10-15W

The average frequency of white light(\nu)=6\times1014 Hz

The average energy of a photon in white light is

\\E=h\nu \\ E=6.62\times 10^{-34}\times 6\times 10^{14}\\ E=3.972\times 10^{-19} J

Number of photons reaching our eyes is n

\\n=\frac{P}{E}\\ n=\frac{4\times 10^{-15}}{3.972\times 10^{-19}}\\ n=1.008\times 10^{4}s^{-1}

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