You are HALVING the exposure time by DOUBLING the shutter speed, therefore you have to DOUBLE the light admitted by the aperture to stay in balance. F11, NOT F22 is the correct adjustment.
Why not F8? F8 is twice as much as F16, right?
Mathematically, 1/8 is twice 1/16, yes, but remember that when you DOUBLE the diameter of a circle you allow FOUR times the capacity, be it a pipe carrying water, or an aperture admitting light. That's two LIGHT VALUES, commonly called "F stops." It's also a 0.30 change in decibels, just so you know.
F11 lies halfway between F8 and F16, more or less. The actual value for F11 is 11.3, but it's usually rounded down for convenience. The formula for the F number is the number of light values ("LV"), where the amount of light either doubles or halves, times the square root of 2, beginning with 1 LV = F1, 2 LV = F 1.4, 3 LV = F2, 4 LV = F 2.8, etc. Check it out in Excel. Some of the big old view cameras went to F90 or even F128!
Think of exposure as sort of a balance where "balance" is when both exposure time and aperture equal "one" unit of exposure, said "unit" being a larger quantity for less-sensitive film, or smaller for "faster" film. It "costs" more "light" when you use "slower" film, BUT you get greater image quality. If you expose with more than this unit you get overexposure, if less, then underexposure. You have to have the "correct change" when you shoot a picture, so to speak.
If you cut one side of your exposure in half as in your question, you have to double the other side in order to stay "in balance," so if the shutter speed number goes UP, the aperture number goes DOWN by the same number of clicks, and vice-versa. Got it? It's a form of exposure time multiplied by the aperture equals the proper amount of light for a "perfect" exposure, defined as one where the original gray scale of the scene is most accurately reproduced.
Play with your camera some more, learn to use your meter, and keep a log of how you exposed each frame of film for use in evaluating results. It will teach you a lot. Also, read Ansel Adams's books on the camera and how to process and print film.
