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

• rocapp
In summary, a typical incandescent light bulb emits approximately 3x10^18 visible-light photons per second. When your eye is fully dark adapted, it can barely see the light from the bulb 10 km away. Using the equation N = n*(d/D), where N is the number of photons per second incident at the image point on your retina, n is the number of photons emitted by the light bulb per second, d is the diameter of your dark-adapted pupil, and D is the distance between the light bulb and your eye, the correct number of photons per second is 9.2x10^4. However, the exact reason for this discrepancy is unclear.
rocapp

## Homework Statement

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.

N = n*(d/D)

## 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

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

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

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.

So then:

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

= 26250 Photons/s

Correct?

Last edited:
That wasn't correct. The correct answer was:

9.2×10^4 s^-1

Anyone know why?

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.

## 1. How do you calculate the number of photons per second on the eye from a source a distance away?

The number of photons per second on the eye from a source a distance away can be calculated using the formula: P = L x A x t x r2, where P is the number of photons per second, L is the luminosity of the source, A is the area of the eye, t is the transmittance of the eye, and r is the distance between the source and the eye.

## 2. What is the significance of finding the number of photons per second on the eye from a source a distance away?

Knowing the number of photons per second on the eye from a source a distance away is important for understanding the intensity of light that is reaching the eye. This can help in determining the potential effects on vision and the potential risks of exposure to certain sources of light.

## 3. What factors can affect the number of photons per second on the eye from a source a distance away?

The number of photons per second on the eye can be affected by several factors, including the intensity and distance of the source, the size and quality of the eye, and the medium through which the light is traveling. Other factors such as the atmosphere and any obstructions between the source and the eye may also play a role.

## 4. How does the number of photons per second on the eye change as the distance from the source increases?

The number of photons per second on the eye decreases as the distance from the source increases. This is due to the inverse square law, which states that the intensity of light is inversely proportional to the square of the distance from the source. Therefore, the further away the source is, the less intense the light will be when it reaches the eye.

## 5. Can the number of photons per second on the eye from a source a distance away be measured experimentally?

Yes, the number of photons per second on the eye from a source a distance away can be measured experimentally using specialized equipment such as photometers or spectrophotometers. These devices can accurately measure the intensity of light and calculate the number of photons per second reaching the eye from a given source at a specific distance.

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