Verified answer

N = f / D

N = f-stop (8.0 and 5.6)

f = focal length

D = diameter of lens

so

5.6 = 50 / D and D = 8.93 mm

also

8.0 = 50 / D and D = 6.25 mm

now

the light admitted is directly proportional to the exposed area of the lens

meaning that it is directly proportional to the square of diameter

(8.93 / 6.25)^2 = 2.04

so changing from 8.0 to 5.6 would let about twice as much light through NOT 1/2

I think the problem should have read "from 5.6 to 8.0"

looking at the f-stop formula you can see that N is inversely proportional to D for a lens of given f

so

the light passed would be inversely proportional to the square of N (f-stop number)

or in this case

light through 8.0 / light through 5.6 = (5.6 / 8.0)^2 = 0.49 or about 1/2

note that higher f/# (N) means less light is let through

setting the f-stop on a camera actually operates a mechanical iris behind the lens

higher number means closing the iris down more

electronic cameras most likely have a computer function to simulate this effect

an interesting effect of closing down the iris is that the light getting to the film or electronic detector is more directional giving a better sense of depth to the resulting photograph because the focal point is more precisely located and smaller differences in distance will become more apparent.

this effect may be less apparent in an electronic camera sad to say

That has to do with digital camera lenses is optics, because of the fact the 1st poster suggested. whether, counting on the digital camera, you might have a pair of different branches in contact -- The digital camera could use an autofocus gadget. this may be infrared, optical, or ultrasonic. -- lower back, counting on the digital camera variety, you might have autos that concentration your lens. That has to do with mechanical couplings.