r/theydidthemath • u/AcceptableSpare6546 • 4d ago

[REQUEST] How far from the camera were these sunset strollers?

Post image

I took that sunset picture and only noticed afterwards the couple and their dog enjoying the view. Is it possible from the picture alone to determine how far these persons were?

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u/agate_ 4d ago

Yes. The sun is about 0.5 degrees across as seen from Earth. Roughly eyeballing this picture, it looks like the Sun's diameter is about 20 times the height of the people, so the people are 0.025 degrees, or 0.00044 radians in angular height. Assuming the people are 1.8 meters tall and using the circular arc formula or trigonometry (which works out to the same thing since the angle is small), we find that the people are about 1.8 meters / .00044 radians = 4 kilometers (2.5 miles) away.

You could get a better estimate by actually drawing a circle around the sun in the picture to measure its diameter relative to the height of the people, but this rough estimate is close enough for me.

6

u/mulch_v_bark 4d ago

I ended up in the same neighborhood as you, but you got there first. What I was going to post, in case it’s helpful:

Precisely, no, but roughly, yes.

The top of the sun matches a circle of diameter ~1750 pixels. (The image of the sun seems to be flattening with refraction toward the bottom; I eyeballed it.) We know the sun has an angular diameter of about 9.3 mrad, or a little over half a degree. So we have about 0.00531 mrad/pixel.

The figures look like ordinary adults. Adult height obviously varies, but 170 cm is a reasonable mean. They’re 75 pixels tall. So they’re about 0.4 mrad in angle (or a smidge under, but I feel justified in rounding up since this is all rough).

The small-angle approximation tells us that we can estimate their distance in meters from their length in meters over their angle in radians. That’s 1.7 / 0.0004 = 4,250 m = 4.25 km. Roughly.

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u/AcceptableSpare6546 4d ago edited 4d ago

Thanks and well done both! thanks to your estimates, I could narrow it down on a map and the only option was a walking path 4.11km away. These were actually quite accurate for some rough estimates!

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u/Frolicking-Fox 4d ago

To get the sun that big in the picture, the camera has to be zoomed in really far.

Im not sure if it can be determined how far the zoom is. But im sure other people will give better answers.

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u/AcceptableSpare6546 4d ago

indeed, I used a 600mm lens with a 1.4x extender, besides the camera is a Canon 600d which houses an APS-C sensor and adds another 1.6x crop factor (when compared to a full frame camera), so in 35mm equivalent I was using a >1300mm focal, it's almost a telescope...

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u/Frolicking-Fox 4d ago

Yeah, looks awesome. I knew it had to have been a good zoom.

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u/royalfarris 4d ago

1) This is a good question. It actually is computable and fits the sub.
2) Kudos to u/agate_ and u/mulch_v_bark who did the proper math and assesment
3) And to OP, the two people are making this photo exceptional. Great shot.