# How many Photons per second are entering the pupil?

• clamatoman
In summary, in this conversation, the number of photons per second emitted by a 100-W lightbulb was estimated using the equation E=hc/λ, resulting in a value of 2.77*10^20 photons. To determine the number of photons entering a person's pupil, the ratio of the surface area of the pupil to the surface area of a sphere with the same radius was used, resulting in a final answer of 6.1*10^9 photons per second. There was some discussion about whether the given answer was correct, but it was determined that the volume of a cone and a sphere with the same radius can be written as the product of their respective surface areas and a factor of r/3.
clamatoman

## Homework Statement

(a)Estimate the number of photons per second emitted by a 100-W lightbulb, assuming a photon wavelength of 550nm.(b) A person can just see this bulb for a distance of 800m, with the pupil dilated to 7.5mm. How many photons per second are entering the pupil?

## Homework Equations

E=hc/λ
h=6.63*10^-34 J s
c=3.0*10^8 m/s
1eV=1.602*10^-19 J
1 watt second = 100 joules

## The Attempt at a Solution

For part (a)
E=hc/λ=(6.63*10^-34 J s * 3.0*10^8 m/s)/(550nm) =3.616*10^-19 J

convert to eV: (3.616*10^-19 J * (1eV/1.602*10^-19J)=2.257 eV per photon

100 watt sec = 100 joules

(100 joules * (1eV/1.602*10^-19J))/2.257eV) = 2.77*10^20 photons

For part (b):
[/B]
Not excatly sure how to proceed. I made a circle and determined the percent of the circumference was the 7.5mm pupil then multiplied that by the total number of photons, but the answer I got did not mach the book.
C=pi*d=pi*1600m=5026.548m
(7.5mm/5026.548m)*2.77*10^20 photons = 4.13*10^14 photons.
The answer in the book is 6.1*10^9 photons.
How can I get to this answer?

clamatoman said:
I made a circle and determined the percent of the circumference was the 7.5mm pupil
Does a lightbulb send out all its photons in a plane?

Ah, I need to consider a sphere, and a conical section of that sphere with the circular base being the 7.5mm pupil. I shall attempt.

Volume of the sphere = 4/3 pi r^3 = 2.14×10^9 m^3
Volume of the cone = pi r^2 h/3 = 0.047 m^3
ratio = 2.196 * 10^-11
2.196 * 10^-11 * 2.77*10^20 =6.1*10^9 protons!
Thanks!

Actually, I believe that the given answer is incorrect. You want to look at the flux of photons passing through the surface area of the pupil per second, so the ratio should be between surface areas, not volumes.

nasu
gneill said:
Actually, I believe that the given answer is incorrect. You want to look at the flux of photons passing through the surface area of the pupil per second, so the ratio should be between surface areas, not volumes.
Wouldn't that come out the same? The volume of a cone is proportional to the area of the base.

I think there is a conspiracy in this so that they come out the same.
The volume of sphere with radius r, $$V_s=\frac{4\pi r^3}{3}=S_s\frac{r}{3}$$
The volume of the cone with height r $$V_c=S_c\frac{r}{3}$$
From the above we conclude that the $$\frac{V_s}{V_c}=\frac{S_s}{S_c}$$ that is that the ratio of volumes equal the ratio of surfaces. The "conspiracy" is that both volumes can be written as the product of the respective surfaces times the same factor ##\frac{r}{3}##.

nasu

## What are photons?

Photons are tiny packets of energy that make up light. They are the basic unit of light and carry electromagnetic energy.

## How does light enter the eye?

Light enters the eye through the pupil, a small opening in the center of the iris. The amount of light that enters the eye is controlled by the size of the pupil, which can change in response to different lighting conditions.

## What affects the number of photons entering the pupil?

The number of photons entering the pupil is affected by the intensity of the light source, the distance from the light source, and any objects that may block the light. The size of the pupil also plays a role, as a larger pupil allows more photons to enter the eye.

## How can we measure the number of photons entering the pupil?

There are various methods for measuring the number of photons entering the pupil, including using specialized equipment such as photometers or spectrophotometers. These devices can detect and measure the intensity of light and calculate the number of photons present.

## What is the average number of photons per second entering the pupil?

The average number of photons per second entering the pupil depends on the lighting conditions and the size of the pupil. On a bright sunny day, it is estimated that around 10^14 (100 trillion) photons enter the pupil per second. In dimmer lighting, the number may be significantly lower.

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