At What Distance Does the Sun Become Invisible to the Human Eye?

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SUMMARY

The discussion centers on determining the distance at which the Sun becomes invisible to the human eye due to insufficient light intensity. In perfect darkness, human eyes can detect approximately 10 photons per second. The Sun emits around 1045 photons per second and is currently 1.5 x 1011 meters away from Earth. By calculating the distribution of photons over a spherical surface, participants aim to find the distance at which the photon flux falls below the threshold detectable by human eyes.

PREREQUISITES
  • Understanding of basic physics concepts, particularly light and photons.
  • Familiarity with the concept of spherical geometry and surface area calculations.
  • Knowledge of how light intensity diminishes with distance.
  • Basic mathematical skills for solving equations related to light distribution.
NEXT STEPS
  • Calculate the photon flux at various distances from the Sun using the formula for surface area of a sphere.
  • Explore the relationship between distance and light intensity in the context of inverse square law.
  • Investigate the physiological limits of human vision regarding light detection.
  • Review the concept of photon statistics and their relevance in optical physics.
USEFUL FOR

Students in physics, educators teaching optics, and anyone interested in the limits of human vision and light perception.

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[SOLVED] Sensing Light at Great Distances

Homework Statement



In perfect darkness, human eyes might be able to sense a point source of light if roughly 10 photons/second strike the retinas. The sun, which is currently 1.5 x 10^11 meters from earth, emits about 10^45 photons/second. Assuming that the pupils of a pair of eyes have a combined area of 1.0 square centimeters, at what distance would the sun become invisible to the unaided human eyes?

Homework Equations



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The Attempt at a Solution



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I've been given this problem in my physics class and have absolutely no clue as to what step needs to be taken first. There are more parts to this question, but figuring out the distance is the first thing that needs to be done. Can anybody offer me any hints as to what I can do to solve this problem?
 
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Imagine a big sphere of radius R around the sun. How many photons are passing through it each second? (Hint: no calculation need be done here, and the answer does not depend on R.)

OK, now, how many are passing through each square centimeter on the surface of this sphere? (This DOES depend on R.)
 

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