Photons collected be telescope apertures

In summary, the energy output of a star on the surface of the Earth provides 5x10^-19 WM^-2 in the visible spectrum. To calculate the number of photons collected per second by a 500mm diameter telescope, the formula used was E=hc/lambda joul/photon, assuming a lambda of 550nm. The result was 4.4 photons per second, which is consistent with a dim star of magnitude +26. This is supported by the fact that a 0.5-metre telescope can only see stars up to magnitude 27. The book showed the answer to be 3x10^7 photons per second, but this may have been a different problem with different coefficients. Overall, the calculations
  • #1
trina1990
24
0
the energy output of a star is such at the surface of the Earth it provides 5x10^-19 WM^-2 in the visible part of the spectrum...
how many photons are collected per second by a 500mm diameter telescope?

i don't know if there's any definite formula to drive the answer...but i tried this way..
stellar flux=5x10^-19WM^-2=5x10^-25 J/S/mm^2
E=hc/lambda joul/photon ( assuming lambda to be 550nm)

then flux/E=1.383x10^-6 photon /S/mm^2

then i found the telescope mirror are to be 4pi (500)^2=3.142x10^6 mm^2
now i derived the number of photons per second collected by the 500mm diameter to be 4.4!

can this be right?
is there any other way to solve this?
 
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  • #2
Aside from the fact that the area of a circle is [itex] \pi r^2 [/itex] (without the factor of 4), I don't see any problems with your math.

I did some rough calculations, and found that a star with that flux has an apparent magnitude of something like +26. Again, I want to emphasize that this was a very rough calculation. I computed the flux of Vega using its stated luminosity and distance (using Wikipedia numbers), and then took m = -2.5log(F_star / F_vega) to estimate the magnitude. I know that Vega isn't used as the zero point for V band magnitudes anymore, but this was just a back of the envelope calculation to show that you're considering a very dim star. In fact Wikipedia says that magnitude 27 is at the limit of what 8-metre ground-based telescopes can see, so it seems plausible that such a star would be invisible in a 0.5-metre telescope (esp. if your detector is the human eye).
 
  • #3
thanks a lot...
the book in which i found this problem showed answer of this problem to be 3x10^7 photons per second...
that's why i got so much stunned with my result...:confused:

but a similar problem with different coefficients shows a result very close to my calculation..
anyway i understood the err of my measuring the area of the aperture...
& with the information you provided from wikipedia, then it's most likely to support the answer...
thanks again
 

What are photons and how are they collected by telescope apertures?

Photons are particles of light that carry energy and information. Telescope apertures, also known as the opening of a telescope, collect photons by allowing them to pass through and enter the telescope's optics.

How does the size of a telescope aperture affect the collection of photons?

The size of a telescope aperture directly affects the amount of photons that can be collected. A larger aperture allows for more photons to enter the telescope, resulting in a brighter and clearer image. A smaller aperture will collect fewer photons, resulting in a dimmer and less detailed image.

Do different types of telescopes have different apertures for collecting photons?

Yes, different types of telescopes have different apertures for collecting photons. For example, refracting telescopes have a lens as their aperture, while reflecting telescopes have a mirror. The design and size of the aperture can vary between different types of telescopes.

What happens to the collected photons once they enter the telescope aperture?

Once photons enter the telescope aperture, they are focused and directed towards the telescope's optics, such as lenses or mirrors. These optics then further manipulate the photons to create an image that can be viewed by the observer.

Can the collection of photons be affected by external factors?

Yes, external factors such as atmospheric conditions and light pollution can affect the collection of photons by telescope apertures. For example, a cloudy or hazy sky can block or scatter photons, resulting in a dimmer image. Light pollution from man-made sources can also interfere with the collection of photons, especially for telescopes located in urban areas.

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