These are examples of a fisheye lens image. It can be a lot of fun to use but there are a few caveats that are important when using a specialty lens like the fisheye. If you position the horizon toward the top of the image, the result is a curved shape like the surface of the earth at a distance…
Here is an example:
If you position the horizon low in an image, the shape will be inverted and give a totally different feeling to an image, such as this example:
If you position the horizon dead center in an image, the distortion is reduced and gives an extreme wide angle effect of about 120 degrees
Here is an image with the horizon almost dead center:
My own fisheye lens is 15mm…
It is also important to note, that if you have an APS-C or smaller sensor, the effects are minimal. I would recommend a fisheye lens only on a full frame camera. There are adjustable fisheye lenses available…this lens can give an image great impact; it can also ruin an image. It must be used with discretion.
Marion, they make fisheye lenses for APS-C sensors too. Mine is a very sharp but reasonably priced manual-everything 8mm Rokinon (the same lens is also sold with Bower and Vivitar brand plates). It is 180° on the diagonal, not circular. The micro 4/3 version is 7.5mm.
Some photos at
https://www.facebook.com/alan.august.3/media_set?set=a.1188313479808.28672.1587475062&type=3
The effect of fisheye on aps-c is not as dramatic as full frame images since the image is cropped.
When using lenses of the same the same focal length on different sized sensors, you are correct. But by using a shorter focal length on the APS-C the same angle of view can be achieved, with greater depth of field resulting from the shorter focal length. Your fisheye lens is 15mm, mine is 8mm.