# Find Photons per second on the eye from a source a distance away

1. Apr 20, 2013

### rocapp

1. The problem statement, all variables and given/known data

A typical incandescent light bulb emits ~3x10^18 visible-light photons per second. Your eye, when it is fully dark adapted, can barely see the light from an incandescent light bulb 10 km away.

How many photons per second are incident at the image point on your retina? The diameter of a dark-adapted pupil is ~7 mm.

2. Relevant equations
N = n*(d/D)

3. The attempt at a solution

I found the above equation on the internet but it didn't work. I tried:

N = Number of photons*(Diameter/Distance)
=3x10^18 s^-1 * (7x10^-3 m / 1x10^4 m)
N= 2.1x10^12 photons/s

This is incorrect. Please help! Thanks!

2. Apr 20, 2013

### technician

The light travels out in all directions so you need to look at the AREA through which the photons pass.
The surface through which the photons pass is the surface of a sphere.
Hope this gets you started

3. Apr 20, 2013

### rocapp

Not sure of this either, but here is my thinking:

Number of Photons/s = (Source Photons/s)/(Surface Area of sphere formed by the distance) * (Surface Area of eye)

Photons/s = (3x10^18 photons/s)/(4*PI*1.0x10^8 m^2) * (4*PI*7x10^-6 m^2)

Photons/s = 2.1x10^5

4. Apr 20, 2013

### Staff: Mentor

The surface area of the eye is wrong (the pupil is like a circle and not a sphere, and 7mm is the diameter, not the radius), but the concept is right.

5. Apr 20, 2013

### rocapp

So then:

((3x10^18)/(4*PI*1.0x10^8)) * (PI*3.5x10^-6)

= 26250 Photons/s

Correct?

Last edited: Apr 20, 2013
6. Apr 20, 2013

### rocapp

That wasn't correct. The correct answer was:

9.2×10^4 s^-1

7. Apr 21, 2013

### rocapp

Anyone know why?

8. Apr 21, 2013

### Staff: Mentor

I don't know. The factor between those two answers is ~3.5. Not pi, not 4, or anything present in the problem statement. Very odd.

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