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I was looking at eclipse footage and I noticed that it doesn't get any noticeably darker until the very end when it suddenly all the light is gone. As the moon blocks out the Sun, I would expect that the brightness would gradually decrease as less of the Sun became visible (e.g. 50% as bright when the Moon covers half of it) however judging from all the videos out there this is not true! I took a look at the Wikipedia article, and it says:

"Partial eclipses are virtually unnoticeable, as it takes well over 90% coverage to notice any darkening at all."

"Even at 99% it would be no darker than civil twilight."

Why would this be the case?

I also found this diagram that may help illustrate my question:

I would expect the graph to be more of a linear shape rather than being so exponential!

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    $\begingroup$ Your eyes adapt to the ambient light to the point that even under totally dark conditions (Bortle Class 1) ...the presence of Jupiter or Venus in the sky seems to degrade dark adaptation. $\endgroup$
    – Count Iblis
    Commented Jun 15, 2016 at 22:10
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    $\begingroup$ @kicker86 The angular sizes of the sun and moon are almost exactly the same (and vary slightly due to orbital eccentricities, which is why we can have both total and annular eclipses). $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Jun 15, 2016 at 22:41
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    $\begingroup$ You are using a log scale graph. Any linear decrease would look like that. $\endgroup$
    – March Ho
    Commented Jun 15, 2016 at 22:59
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    $\begingroup$ @MarchHo, on a linear scale, the intensity graph wouldn't be a straight line (the Sun's surface viewed from Earth isn't of uniform apparent brightness, and the boundary between the Sun and the Moon isn't of constant length). I'd expect it to be roughly quadratic. $\endgroup$
    – Mark
    Commented Jun 16, 2016 at 18:19
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    $\begingroup$ An anecdote: I was in the north of England during the 1999 solar eclipse, which was not total in that part of the country. When the Sun was a crescent it didn't seem that dark to me, but a hedgehog came out of the bushes and started wandering around the park. So evidently it was dark enough for some nocturnal animals to think night was falling, even if it didn't register as such to human perception. $\endgroup$
    – N. Virgo
    Commented Jun 19, 2016 at 4:39

4 Answers 4

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Human perception is generally logarithmic. For example, the perceived loudness of a sound is measured using decibels, where an decrease of $10 \text{ dB}$ divides the sound intensity by $10$. So if the eclipse were heard instead of seen, "90% coverage" might mean reducing the intensity from $120 \text{ dB}$ to $110 \text{ dB}$, a small change.

Perceived brightness is the same way. There's a huge range of light intensities that we see every day: direct sunlight is ~100 times brighter than indoor lighting, though both look fairly bright to us. So a 90% reduction wouldn't make the sky look dark at all.

The shape of the graph 'looks like an exponential' because the $y$-axis is the log of the intensity. This is done so the graph somewhat represents "perceived brightness" vs. time.

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    $\begingroup$ Another thing to keep in mind is that if you were looking at footage of an eclipse, the camera might be automatically adjusting its settings to compensate for the fading. Cameras aren't nearly as good at doing this as humans are, but they can certainly compensate for a 10x reduction. $\endgroup$
    – knzhou
    Commented Jun 15, 2016 at 22:07
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    $\begingroup$ Nice answer, but you shouldn't go out on a limb with the statement about cameras. The f-stop range of the human iris is only between around f/2.1-f/8.3, modern camera lenses are far better than that. Cameras shutter speed is highly variable between fractions of a thousands of a second to virtually infinite, which makes them superior at fast and very low light acquisition. The main limitation in many cameras is the CCD/CMOS sensor full well capacity, which is chosen smaller in most consumer/semi-pro cameras than it should be because of the small pixel size. $\endgroup$
    – CuriousOne
    Commented Jun 15, 2016 at 22:16
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    $\begingroup$ Of course... those are only good-weather shooters... the physical limitation of the small size can't be overcome. The performance of a professional camera is far superior to the human eye... where things are falling apart, still, are the displays. There are no displays that can show the full dynamic range that can be recorded with the right camera or that the human eye can cover thanks to the incredible image processing in our brains. $\endgroup$
    – CuriousOne
    Commented Jun 15, 2016 at 22:21
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    $\begingroup$ @CuriousOne: The human eye can perceive light textures and dark textures in a single scene, even when the contrast between them is higher than 35mm Tri-X can really capture (I used bracketed exposures to shoot a building where I could see bricks in both sunlit and shadowed areas, and managed to simultaneously overexpose the sunlit parts and underexpose the shadowed parts). I don't know that I could see bricks in both parts "simultaneously", but could look between the two parts without much difficulty. $\endgroup$
    – supercat
    Commented Jun 15, 2016 at 23:26
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    $\begingroup$ @Crowley Don't forget that your brain lies quite a bit about what your eyes see. The signal coming from the eyes is going through a lot of post processing, and it's assembled in the total picture maintained in your "vision perception". This includes combining data from different exposures and focii; use a HDR camera and you'll get pretty shots of the Moon too. Also note that there's two aspects to camera superiority - 1) capturing the scene, 2) capturing the scene wrong enough to simulate human vision. 2) is quite hard - cameras see reality better than we do but that's a disadvantage here. $\endgroup$
    – Luaan
    Commented Jun 16, 2016 at 14:54
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The graph looks exponential because the vertical axis is logarithmic! If you were to re-plot it as linear lumens per square meter, it would be much more v-like, or even u-like.

It so happens that a logarithmic plot matches our subjective perception of light intensity better than a linear one would. That's a result of our eyes having evolved to work well in an extremely wide range of different amounts of light.

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  • $\begingroup$ Is that the same as the inverse square law? $\endgroup$
    – Tim
    Commented Jun 16, 2016 at 19:35
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    $\begingroup$ This is key - our eyes adjust their pupils so the effective light entering the eye is roughly the same. It would take a bit of darkening before the light drops off to the point where the pupils are at their largest and the eye can no longer counteract the darkening. $\endgroup$
    – user57109
    Commented Jun 16, 2016 at 19:57
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Based on my own anecdotal evidence, it doesn't. Several years ago there was a partial solar eclipse in my area. I don't remember precisely how much of the sun's disk was covered - it wasn't much, surely nowhere near 90% - but I do remember getting out of the house in the morning, thinking "hmm, it's quite dark today", then having the eerie realization that the sky was perfectly clear, with none of the haze or clouds I was expecting. So yes, the darkening is noticeable.

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  • $\begingroup$ This was my exact reaction. We had a significant solar eclipse here recently, and it was easily noticeably darker when the sun was only about a third covered. $\endgroup$
    – T.J. Crowder
    Commented Jun 19, 2016 at 5:35
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Any shadow, either that of a small ball or a celestial body(especially spherical) consists of two parts umbra and penumbra. They are separated by a distinct border. Think of the moon(object) casting its shadow on the earth(screen) due to the sun(light source). Due to relative distances the moon's umbra is small, so only a small portion is in extreme darkness. On the other hand a relatively large penumbra of even darkness is formed.This darkness is the same in all places of sufficient proximity from the epicentre of the eclipse regardless of how much of the sun is blocked out by the moon when viewed from the location in question.

So, in response to your question when the sun appears nearly fully covered from the location in question it means that location comes under the umbra region of the shadow. That's why it suddenly gets dark.

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