# Intensity of light entering eye

1. Oct 15, 2011

### Weistber

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. Oct 15, 2011

### Spinnor

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.