Why is that the wider the aperture of a lens is, the more we can see through narrow cracks and crevices?

Question

Example I took at 85mm f/1.4 on APS-C sensor:

Answer 1

Sometimes a picture, even a crudely drawn one, is worth a thousand words.

Answer 2

That is not entirely true:

You can see better through them because the depth of field (DOF) is shallower. If you focus on the object behind, a wider aperture allows the foreground to be blurred more heavily:

^{Legend: BG ... background; FG ... foreground.
Photos were made handheld (so framing and focus might nit be 100% accurate), no post-production (except crop and resize).
All photos made at 105mm.}

While the sample with the most blurred slats (the first) almost diminishes them, the overall scene became somewhat darker where the blur appears.

Answer 3

The "entrance pupil" is the open aperture you are seeing from the front lens, basically with the diameter f:n (f being the focal length and n being the aperture number). This is basically a disk, every point of which is looking out at any imaged point in the world. The larger this disk is, the more angles are there from which this disk gets a peep at the world. Basically you can draw a cone from the edge of this disk to any point in in-focus distance, and this cone (or its continuation) is how light arrives in the camera for each point on the sensor corresponing to the cone to its in-focus point in the focusing distance. The more an object is out-of-focus, the less is its contribution to any particular cone and the more cones it contributes to. To block an in-focus object point entirely from view, you need to block its entire cone to the entrance pupil. With a large aperture and a close blocking object, only solid objects will do the trick.