How many photons?

How many photons???

1) A typical incandescent light bulb emits 3x10^18 visible-light photons per second. Your eye, when it's 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 6mm.

Some relevant formulas I found from the textbook are E=hf, c=(lambda)(frequency), lambda=h/(mv)
But none of the above formulas seem to apply by any means to this weird question. Why does the distance 10km matter? Why does the diameter of an eye matter? How can I even use them?

I am really lost and confused. I hope that someone would be nice enough to help me out. Thank you so much!

Answers and Replies

Doc Al
Mentor
Imagine that the light bulb is sending out all those photons in all directions equally. What fraction would make it into your eye at a distance of 10 km? One way to figure it out is to think of a huge 10 km radius sphere surrounding the light bulb--compared to the surface area of that sphere, how big is the surface area of your pupil?

Imagine that the light bulb is sending out all those photons in all directions equally. What fraction would make it into your eye at a distance of 10 km? One way to figure it out is to think of a huge 10 km radius sphere surrounding the light bulb--compared to the surface area of that sphere, how big is the surface area of your pupil?
Thanks for your reply!

But what is the surface area of the eye? Should it be considered full sphere, a semi-sphere (half sphere), or something else?

Dick
Science Advisor
Homework Helper
The photons have to go through the pupil. That's the relevant area, a disk 6mm in diameter.

Thanks for your help! I got it!

I was curious as to the answer. I used to do research in biophysics/vision. Under really good experimantal conditions, the human eye can detect between 1 and 5 photons, an amazing sensitivity when you consider the dynamic range of the system.

Hi all,
discussion is goin on nicely...
I had que. whether this number of photons that our eye can detect is per unit area or on the whole surface of eye...?

Hi all,
discussion is goin on nicely...
I had que. whether this number of photons that our eye can detect is per unit area or on the whole surface of eye...?

Most of these experiments I recall were done in dark adapted volunteers using all of the eye. But in theory, all you need is capture of one photon by one rhodopsin photopigment molecule which sets into motion a biochemical cascade with gain measured in the millions.