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Weistber
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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.
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.)
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
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.
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.
Homework Statement
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.)
Homework 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
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.
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