I would like to know how large a telescope's mirror aperture would need to be, that is pointed squarely at Sirius to equal the light intensity at the focus of a 5 inch glass lens of our Sun? I well know that such a telescope is impossible. I am trying to grasp better the true dimness of starlight from a somewhat unorthodox perspective. Thank you.
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The apparent magnitudes of Sirius and the Sun are $m_\mathrm{Sir} =$ –1.46 and $m_\odot =$ –26.74, respectively. That means that the Sun is brighter than Sirius by a factor of $$ f = \frac{F_\odot}{F_\mathrm{Sir}} = 10^{-(m_\odot-m_\mathrm{Sir}) / 2.5} = 1.3\times10^{10}. $$ The area of your telescope should be larger than your 5" glass lens by the same factor to receive an equal amount of light. Thus, your telescope should have an aperture of $5\!\!" \times \sqrt{f} = 14.5\,\mathrm{km}$.
Extrapolating (linearly in lin-log space) the evolution of telescopes from Galileo's 1620 telescope, the figure demonstrates that Roger H. will have his telescope ready by the year 2555, May 21 9:53 pm$^\dagger$.
$^\dagger$± a few minutes.
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$\begingroup$ Well… our largest telescopes today are a factor of 1e3 larger than the first telescopes used, 400 years ago. So to reach another factor of 1e5 larger will probably take a few years :) $\endgroup$– pelaCommented Nov 22, 2016 at 11:38
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$\begingroup$ Roughly 600 years, to be specific, given the evolution of telescopes through the last 400 years :) $\endgroup$– pelaCommented Nov 25, 2016 at 20:02