Let's see if my vision of the moon illusion is correct:

The true cause of the moon illusion?

As shown in the figure, the blue line is the lens, w is the height of the object, x is the height of the image, v is the distance of the image, u is the distance of the object, and f is the focal distance. The red line is the path of light.

The relationship between u, v, f is

1 / u + 1 / v = 1 / f

and so

f = uv / (v + u) (1)

The observer's eyes are constant, so v is fixed. The distance between the observer and the object is constant, so u is also fixed. Once v and u are fixed, we can tell from equation (1) that f is also fixed. If v is fixed and u decreases, then f also decreases.

Know about similar triangles:

x / w = (v-f) / f = v / f-1

and so

x = w (v / f-1) (2)

According to formula (2), if v and w are fixed, x will increase when f decreases.

When the observer observes the moon on the horizon, due to the influence of mountains and trees, f is smaller than that when observing the moon at zenith. According to formula (2), we can know that when f decreases, x increases. Then the observer will feel that the moon on the horizon is larger and closer than the moon at zenith.

I think this is the reason for the moon illusion.

Simple calculation

When looking at nearby trees with your eyes:

u = 200 m (assuming 200 m from the tree)

v = 0.024 m (diameter of the eyeball, assumed length of the image)

w = 10 m (assuming the tree is 10 m high)

f = uv / (v + u)

= 0.0239971 m

x = w (v / f-1)

= 0.0012m = 1.2mm (height of tree image)

When looking at the zenith moon (without the influence of the trees on the ground) with the eyes:

u = 380000000 m (distance from the observer to the moon)

v = 0.024 m

w = 3476000 meters (moon diameter)

f = uv / (v + u) = A (we set this focal length to A)

x = w (v / f-1)

= 0.000219537 m = 0.219537 mm

In the direction of the horizon, if you look at the moon at the focal length of the observation tree:

f = 0.0239971 m

x = w (v / f-1)

= 420,067 m

Observing the image of the moon at the zenith is 0.219537 mm, and observing the image of the moon on the horizon is 420.067 m, showing a great difference between the two. So using a focal length less than A will "magnify" the moon.

Of course, the eyes generally do not observe the moon with a focal length of 0.0239971 m. Because the image may not be clear. But if the moon image is not clear at this focal length, then the eyes will adjust the focal length. Adjust to a focal length that is clear to the image. This focal length is less than A, but it is the focal length for clear images. Because the moon is so far away, the depth of field of the moon image is very large. Therefore, there is a focal length that is smaller than A and can display images clearly. So the moon illusion is caused by a relatively short focal length. I think that's why the illusion of the moon.

reference

https://en.wikipedia.org/wiki/Moon_illusion