Unfortunately the F707 does not give us the focal length of the zoom lens while composing and shooting a picture. This makes it difficult to reset the camera to a previous lens setting. (It does, however, give the focal length in the EXIF file, but only after downloading to a computer.) Even worse, the F707 resets the zoom to full wide (9.7mm) whenever you turn it on. (Interestingly, when you shut it off, the lens contracts to the full telephoto setting).
I had hoped the F707 used a stepper motor (a kind of digital moving motor) to move the lens assembly, thus offering the possibility to calculate the precise focal distance by measuring the steps. Unfortunately, Sony opted for a cheaper DC motor (you can see the analog movement while looking at the front of the lens while depressing the zoom button).
Fortunately the zoom bar offers some hope to calculate the focal length. If you notice that while depressing the zoom button, the marker in the zoom bar jumps in seemingly discrete steps. In fact there are precisely 15 steps within the zoom bar; 10 steps are for the actual zoom and 5 steps for the digital zoom. There are, of course, an infinite number of zoom positions between these jumps, but in actuality you can only stop in a finite number of them depending on how quickly you can tap the zoom button. (I can manage between 4 to 11 mini positions between each bar marker jump.)
I took 10 sets of photos for each jump position and wrote down the focal lengths. I then averaged the numbers to determine the median focal distance for every jump. The chart above shows the final average numbers.
The focal length numbers with the tolerances are as follows:
9.7 (+.0 -.0) Full wide
10.8 (+.1 -.1)
12.7 (+.1 -.2)
15.1 (+.2 -.2)
18.3 (+.5 -.2)
22.5 (+.3 -.3)
28.2 (+.3 -.5)
35.1 (+.5 -.4)
43.6 (+.5 -.6)
48.5 (+.0 -.0) Full telephoto
Notice that the tolerance error increases toward the Telephoto direction.
I also made measurements of each jump by starting from the 48.5 setting and going toward the 9.7 setting. The numbers are different! This is because there is a hysteresis error due to the DC motor movement. The F707 apparently uses the full wide position as the home position to reset the position. This perhaps explains why Sony opted to automatically set the lens to full wide whenever you turn on the camera.
The numbers did not come out as precisely as I would have liked, but perhaps this information might serve some use to someone. Also note that my numbers relate to only my camera. Because of unknown manufacturing tolerances, your camera may not agree with my numbers.
Jim