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A bit of math: what should the DIY copy stand height, to focus the smartphone camera on the flat A5-size object, that the object is photographed at 1:1 magnification? Smartphone camera - in the regular mode (not macro mode). It's assumed that the copy stand height will be a fixed height, not adjustable.

Edit: More precisely, the question is more about trigonometry, what I need is actually height of isosceles triangle. But I don't know angle of view of a smartphone camera, and lens field of view parameter.

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    \$\begingroup\$ Do you want the image on the sensor to be 1:1 or do you want the image as presented (enlarged to some given size) to be 1:1? The sensor in a phone is quite small. If you want the object to fill the frame when the picture is enlarged to A5 size, that is quite different. In your comment to Romeo Nirov it seems you want the second. Instead of calculating, I would just measure it. Get an A5 sheet of paper and move the phone until the paper just fills the frame. \$\endgroup\$ Feb 12, 2022 at 15:49
  • \$\begingroup\$ And to add to @RossMillikan, the distance depend on the lens of your phone \$\endgroup\$ Feb 12, 2022 at 15:56
  • \$\begingroup\$ I meant a minimal distance from which the complete A5 size object fill the frame, without cutting the edges and without zoom function. It may vary depending on the phone lens, so just in general. \$\endgroup\$
    – triwo
    Feb 12, 2022 at 16:16
  • \$\begingroup\$ Based on your comment, what you are trying to do is clearly not 1:1 magnification photography (i.e. not macro photography). This is a question about basic trigonometry (SOHCAHTOA), using the (horizontal/vertical) angle of view of a smartphone camera. Please edit/correct your question title. \$\endgroup\$
    – osullic
    Feb 13, 2022 at 13:34

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If you want to have A5 to be 1:1 you need sensor with size A5. This is by definition 1:1 magnification ratio (object is projected on the sensor with the same size as reality).

The maximum size object you can reproduce with smartphone will be something like 6.17mm by 4.55mm (sensor 1/2.3).

If you want to get the entire object in the frame it depend of angle of view (focal length of the lens). For Samsung S20/OnePlus 8T (~120 degree angle of view) will be around 74mm (this is with wide angle lens where you can expect some geometric distortions). For standard lens of OnePlus 8T the distance is around 20cm

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  • \$\begingroup\$ Thanks. I have to clarify: I meant just focusing on a full A5 size object into the frame, without cutting the edges. \$\endgroup\$
    – triwo
    Feb 12, 2022 at 15:49
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For this kind of thing, I've been using Rui Salgueiro's field-of-view calculator for years. You will need to determine the sensor size and focal length of the smartphone camera – hopefully the manufacturer publishes this data. The above website will then give you the horizontal/vertical angle of view. You already know the dimensions of the A5 sheet of paper, so then it's just a matter of using the formula tan θ = Opposite / Adjacent. Drawing a schematic and labelling angles/lines may help.

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  • \$\begingroup\$ I've always maintained that photography is the art for mathematicians \$\endgroup\$
    – osullic
    Feb 13, 2022 at 20:11
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@Romeo Ninov comment about a 1:1 magnification is correct. Your problem is a totally different concept.

What you need is simply put, fill the screen when photographing a piece of paper.

And for that matter, there is no way to know which is the optimum distance.

You could do some math knowing the field of view, with a specific lens of a specific smartphone.


what I need is actually height of isosceles triangle.

You do not know if what you will get is an isosceles triangle. IF that was the case you could simply use something like this:

https://www.calculator.net/triangle-calculator.html?vc=60&vx=&vy=&va=60&vz=148&vb=&angleunits=d&x=62&y=20

Assign a number for the base, and let the 3 angles be 60.


But again, the angles are very specific to the field of view of the lens.

Save yourself some headaches and simply take a ruler and play with your smartphone to figure out the ideal distance to your paper.

Try using the longest focal length you have that can focus on the paper.

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Experimentally, you are quite far from "macro": on my phone , you have to be 22cm away from the paper while the closest focus distance is around 7cm. While I assume other phones to yield similar distances, this will vary with actual focal length and sensor combination, so I don't think you can make a one-size-fits-all stand that does an exact fit of the A5.

And in practice, adjustable height can be useful (page of thick book, top of box...).

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