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Intensity of light entering eye

  1. Oct 15, 2011 #1
    Hello all,
    I came across this question in mastering physics and simply could not solve it. I asked for the answer to the question and decided to move on.


    1. The problem statement, all variables and given/known data
    You are standing 1.7m from a 100-W lightbulb.

    If the pupil of your eye is a circle 5.0 mm in diameter, how much energy enters your eye per second? (Assume that 5.0% of the lightbulb's power is converted to light.)


    2. Relevant equations
    Energy of a beam of light =(Energy Density)(Volume):
    U = UEM(Area X Speed Of Light X Change in time)
    U = UEM(AcΔt)

    Intensity:
    I = U / (AΔt) = UEMc

    3. The attempt at a solution

    I decided that the energy of the beam must be equal to 5% of the wattage of the light bulb.

    U = (5/100)*100W
    = 5 J/s

    I then found the energy density (UEM) by dividing U by volume (Area x distance from light source).

    UEM = U / (AcΔt)
    = (5) / (Pi((2.5*10^-3)^2) x 1.7)
    = 149792.88 J/M^3

    From this I derived the light intensity.
    I = UEMc
    = (149792.88) x (3 x 10^8)
    = 4.49 x 10^13 J/s

    At this point I was completely lost. The intensity is simply too large and has exceeded the amount of energy the light bulb can provide. I tried following through to the answer by multiplying intensity by area of the pupil, but the number was still far larger than the energy provided by the bulb. I tried using 5J as the value of UEM, but that didn't give the answer either.

    The answer I received from mastering physics was 2.7 microjoules. Please explain to me the concept, I think i've misunderstood it and my notes aren't helpful at all. I don't need a worked answer, just an explanation of how I've misinterpreted the question or concept. Thank you, I'm starting to think I'm not cut out for this, spent three hours on such a simple question.
     
    Last edited: Oct 15, 2011
  2. jcsd
  3. Oct 15, 2011 #2
    You wrote,

    U = (5/100)*100W
    = 5 J/s

    Let that power, call it P, fall uniformly on the inside of a sphere of radius 1.7m. What is the area of that sphere, call it A_s and call the area of your eye A_e. Those are the three numbers you have to deal with, P, A_s, and A_e. How should you combine those numbers to get the power in the eye, call it little p? You know little p will be much smaller then P and when you combine the numbers you must have units of power.
     
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