If a 100-W lightbulb emits 3.5 % of the input energy as visible light (average w

Question

If a 100-W lightbulb emits 3.5 % of the input energy as visible light (average wavelength 550 nm) uniformly in all directions.

Part A

How many photons per second of visible light will strike the pupil (4.0 mm diameter) of the eye of an observer 1.6 m away?

Express your answer using two significant figures.

N1t =_______ photons/s

Part B

How many photons per second of visible light will strike the pupil (4.0 mm diameter) of the eye of an observer 1.2 km away?

Express your answer using two significant figures.

N2t =_________ photons/s

Explanation / Answer

a) Intensity of light at 1.6 m away I = P / A

I = P / (4pi R^2 )

= (3.5 W) / (4pi (1.6)^2) = 0.1088 W /m^2

No. of photons striking to that surface

N = IA / Ephoton

where A = area of surface at which photon striking

and E = hc / lambda

N = (I A lambda) / hc

N = (0.1088 x pi x 0.002^2 x 550nm) / (1240 nm-eV x 1.60 x 10^-19 J/eV) = 3.79 x 10^12 photons

b)

Intensity of light at 1.2 km away I = P / A

I = P / (4pi R^2 )

= (3.5 W) / (4pi (1200)^2) = 1.934 x 10^-7 W /m^2

No. of photons striking to that surface

N = IA / Ephoton

where A = area of surface at which photon striking

and E = hc / lambda

N = (I A lambda) / hc

N = ( 1.934 x 10^-7 x pi x 0.002^2 x 550nm) / (1240 nm-eV x 1.60 x 10^-19 J/eV) = 6737931.23 photons

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