Intensity of light entering eye

In summary, the conversation discusses a question from mastering physics about the amount of energy that enters the eye from a 100-W lightbulb. The person tried various calculations but was unable to arrive at the correct answer of 2.7 microjoules. They were then given a hint to consider the area of a sphere and the area of their eye to calculate the power in the eye, and were reminded that the final answer should have units of power.
  • #1
Weistber
4
0
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.

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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  • #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.
 

What is intensity of light entering the eye?

Intensity of light entering the eye refers to the amount of light that reaches the retina of the eye. It is measured in units of illuminance, which is the amount of light energy per unit area.

Why is intensity of light entering the eye important?

The intensity of light entering the eye determines how bright or dim an object appears to us. It is crucial for our vision as it allows us to see objects clearly and perceive their color and details.

How is intensity of light entering the eye measured?

The intensity of light entering the eye can be measured using a light meter, which records the amount of light in a specific area. It can also be estimated by comparing the brightness of different objects or by using a light source with a known intensity.

What factors affect the intensity of light entering the eye?

The intensity of light entering the eye can be affected by several factors, including the distance between the light source and the eye, the angle at which the light enters the eye, and the presence of any obstructions or filters that may alter the light's intensity.

How does the intensity of light entering the eye impact our vision?

The intensity of light entering the eye determines the amount of light that is available for the eye to process, which can affect our visual acuity and color perception. Low intensity light can make it difficult to see in dimly lit environments, while high intensity light can cause glare and discomfort.

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