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

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In summary, the problem asks to determine the distance at which the sun becomes invisible to the unaided human eyes. This can be calculated by considering the number of photons emitted by the sun and the area of the pupils of a pair of eyes. By imagining a sphere around the sun and calculating the number of photons passing through it per second, and then dividing that by the surface area of the sphere, the distance at which the sun becomes invisible can be determined.
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UMich1344
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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.)
 

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

1. How do we sense light at great distances?

We use specialized instruments called telescopes to detect and amplify the faint light from distant sources. These telescopes are equipped with lenses or mirrors that gather and focus the light, allowing us to see objects that are millions or even billions of light years away.

2. What types of light can be detected at great distances?

Telescopes can detect a wide range of light, including visible light, radio waves, infrared light, ultraviolet light, and X-rays. Each type of light carries different information about the objects it comes from, allowing scientists to study a variety of phenomena in the universe.

3. How do we measure the distance of objects based on the light we receive?

Scientists use a variety of techniques to measure the distance of objects based on the light they receive. These include parallax measurements, brightness measurements, and the use of standard candles – objects with known luminosity that can be used as a reference point for measuring distance.

4. Can we sense light from the beginning of the universe?

Yes, we can detect light from the early universe using powerful telescopes such as the Hubble Space Telescope and the James Webb Space Telescope. These telescopes can capture light that has been traveling for billions of years, allowing us to study the origins and evolution of the universe.

5. What are some current challenges in sensing light at great distances?

One of the main challenges in sensing light at great distances is the interference caused by Earth's atmosphere. This can be overcome by using space-based telescopes or ground-based telescopes equipped with adaptive optics. Another challenge is the limited sensitivity of current telescopes, which can be improved with the development of new technologies and instruments.

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