I'm admittedly rather new to the world of interchangeable lenses, and have just purchased a Panasonic GH4 and adapted it to a full frame lens with a Metabones speed-booster. I've been using a 50mm lens, under the impression that what I was seeing through the viewfinder was truly a 50mm shot. I have since read that a Micro 4/3s sensor shoots everything effectively 2x the focal length of the lens, so is my 50mm truly acting as a 100mm lens, despite my adapter? I apologize for my ignorance, and appreciate any light you can shed.
You speak of two different factors.
The 2x crop factor equivalence of 4/3 sensors is based on the sensor size. The 4/3 camera sensor has a crop factor of 2, meaning it has a diagonal 1/2 the dimension of a full frame camera, so the smaller sensor "crops" the field of view seen to be only 1/2 of the field of view (1/2 of the diagonal dimension). The lens is not changed in any way by mounting it on a smaller sensor. The reduced field of view is instead due to the smaller sensor size (too small to capture the full image from the lens). This is a very simple concept. The cropped sensor means the image is cropped smaller, and the smaller image is missing the outer extents of field. See https://www.scantips.com/lights/cropfactor.html about Crop Factor.
The Panasonic GH4 has a 4/3 sensor with crop factor of 2. That means that its smaller sensor sees a smaller cropped field of view, which means its 50 mm lens sees the same field of view that a full frame camera with a 100 mm lens would see (if standing in the same place). The 100 mm equivalence describes the full frame camera, NOT the 4/3 camera. The 4/3 camera in this case is still using a 50 mm lens. It sees what it sees, but we can say that the cropped smaller field of view that it sees does compare to a full frame sensor with a 100 mm lens (if 2x crop factor). If both cameras used the 50 mm lens, the smaller sensor simply crops the view smaller than the larger sensor would see (uncropped).
The Metabones is an optical adapter, with glass optics in it, which does change the effective focal length of the lens combination. Its 0.7 factor means the lens combination becomes 50 mm x 0.7 = 35 mm equivalence. The field of view is 1/0.7 or 1.4x wider (wider than what this sensor saw without the adapter).
So the 2x crop factor 4/3 camera, if using a 0.7x optical adapter, would have a equivalent crop factor of 2 x 0.7 = 1.4x crop factor. The meaning is that the field of view (4/3 with adapter) then would compare to a full frame camera using a 50 x 1.4 = 70 mm lens.
It crop factor does NOT mean it becomes a 70 mm lens. The sensor cannot change the physical lens. It remains a 50 mm lens, but now with 0.7 adapter that does change the combination to become a 35 mm lens combination. That is the numerical data that applies. But the 2x crop sensor means that the field of view this combination sees compares to a full frame camera if using a 70 mm lens. But again, it certainly is not a 70 mm lens on the 4/3 camera. The lens is clearly marked 50 mm, and the adapter is clearly marked 0.7x.
So this lens on the 4/3 body remains a 50 mm lens with an 0.7x optical adapter making it act like a 35mm lens (on a 4/3 body). Due to crop factor, the field of view acts like a 70 mm lens on a full frame body. But the combination acts like a 35 mm lens on the 4/3 body.
If you have years of past experience with full frame bodies and lenses, this is good information to know, your experience can know in advance what the 4/3 body will do then.
If not familiar with full frame use, then this full frame equivalence probably has little meaning to you.
We do think of the crop factor as multiplying the focal length to a longer equivalence. It doesn't of course (except as compared to full frame), but it would superficially appear that we do get telephoto pictures from the cropped sensor.
However, the same effect is true of any cropping.
Take any image in your photo editor, and zoom in to double size. It then shows a reduced (cropped) field of view, but the smaller image is now enlarged more to same original size again. This necessary greater enlargement of a cropped image does appear as if a telephoto effect, but it is only a smaller image which is necessarily enlarged more back to same size. The enlargement is done afterwards, but it is a reduction in the camera.
Since the beginning, camera sizes have risen and shriveled based both on improvements in technology. As the 20th century dawned film had sufficiently evolved making miniature cameras possible. The first truly functional miniature was the Leica designed in 1913 and marketed in 1923. This still camera accepted 35mm wide motion picture film which by that time was abundant. Leica’s chief engineer, Mr. Barnack, set the format size at 24mm height by 36mm length. This format became the de facto standard for miniature cameras. Today’s top gun digitals, classed as “full frame”, embrace this format size.
Technology marches on. Cameras continue to shrink. The 4/3 format measures 13mm height by 18mm length. You need to know that the vast majority of photographers we hold in esteem were reared on the full frame 35 mm film cameras. They know everything about how this camera responds when different focal lengths of lenses are mounted. When they transition to smaller formats, might they not appreciate a helping hand?
Crop (magnification) factor to the rescue: To find equivalency of lenses between formats, we evaluate the corner to corner measure of one to another. Thus -- the full frame measures 24mm height by 36mm length. Its diagonal measure is 43.3mm. The 4/3 format measures 13mm height by 18mm length. The diagonal measure is 21.6mm. Now we divide to find the crop factor 43.3 ÷ 21.6 = 2. Viola! The crop (magnification) factor is 2.
What does this tell us? If we mount a 25mm lens on a 4/3 camera, the angle of view delivered will be the equivalent of 25 X 2 = 50mm. Another way to use this factor, we mount a 200mm on a full frame, what is its equivalent when using a 4/3 camera? Answer 200 ÷ 2 = 100mm. Also, the inverse of the crop factor 2 = 1/2 X 100 = 50. In other words the 4/3 is 50% of the size of a full frame.
I personally don’t like this concept of crop factors. We did not use them when we transitions from 4X5 view cameras to the smaller formats. Besides, you younger folks likely never became attached to the full frame format that is so revered.