Tiny People, Tiny Cities

Have you ever wondered why things that are further away look smaller? Click through to learn more about angles and how to use them to take cool funky photographs :)

Have you ever wondered why things that are further away look smaller?

The size of the objects you see (and photograph) depends on the angle it subtends from your eye. Hence if we have two objects of the same size, the furthest one covers a smaller angle and seems smaller.

If you have a large object in the background and place a smaller object much closer to you it will look even larger!! This is what I did one day while at Kurnell. I could see the Sydney skyline from the beach and there were a lot of kitesurfers doing jump and tricks so I thought to myself “how awesome would it be if they were jumping over the city?!”. All that was left then was patience… I had to wait for the kitesurfer to jump again, he had to be close enough to me so that he was larger than the buildings, and then I had to frame and time it correctly!! It probably took me about 200 shots but in the end I got what I wanted :)

Note how the background is out of focus but the kitesurfer is in focus. This is because of the largish apperture used when taking the photo (f/7.1), which makes the depth of field quite shallow. More on depth of field and it’s relationship to aperture another time :)

To wrap this up let’s do a little calculation using trigonometry. According to Wikipedia:

“Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles”

The relationship we need for this calculation is the tangent of an angle, which is defined as:

$\tan(angle)=\dfrac{opposite}{adjacent}$

Say, for example, we want to take the photo of one person eating another person (like in the picture below). And let’s suppose that the person being eaten is 2 metres tall (h_real). The person closest to the camera is 1 metre (d_close) away from the camera and we want to make the person furthest away look as if he is like only 20 cm tall (h_apparent). The key to figuring out how far away the second person has to be (d_far) is the following:

The 20 cm in apparent height and the 2 m in real height of the organge person subtend the same angle from the camera.

If two angles have the same tangent it means they are the same angle! Hence, from the diagram below we can conclude:

$\tan(angle)=\dfrac{h_{apparent} / 2}{d_{close}}=\dfrac{h_{real} / 2}{d_{far}} \rightarrow$

$d_{far} = d_{close} \cdot \dfrac{h_{real}}{h_{apparent}} = 1m \cdot \dfrac{2 m}{0.2 m} = 10 m$

So you can see that in our rough calculations the person standing behind has to be 10 metres away from the camera!! This is something you could have figured out by just going out there and trying it out, but this way you can plan ahead and have an estimate of how much space you are going to need for your particular idea.

Have you taken any photos playing around with perspective? Please share them with me, I’d love to see them :) And I would also like to know what you thought of the physicsy part of the post? Were the maths too hard or was it all easy peasy?

xx Ana :)

4 thoughts on “Tiny People, Tiny Cities”

1. Nice explanation, understandable and nice graphics. You make these graphics yourself? compliments.

watchingphysics.net

Like

• Ana says:

Thank you! Yes, I make all the diagrams myself using Adobe Illustrator. Thanks for reading!

Like