Now you might want to compare its field of view to some other lens on some other sensor. And it is true that the smaller cropped size of the DX sensor does reduce its field of view, so that (if with a 50mm lens) its reduced field of view compares to what a 75 mm lens on a 35mm film frame would see (or a FX frame is the same size as 35mm film). But if your lens is marked 50mm, it always remains 50 mm lens on any sensor.

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I know that the effective focal length of the 50mm FX lens is actually 50 x 1.5 = 75mm, because I'm shooting with an APS-C sensor.

The DX frame was adopted from a failed film format that Kodak introduced along with most of the major camera companies is the 1990’s. The idea was to make a hybrid cameras that used photo film with a transparent magnetic coat. Data was recorded both photographically and electronically on the film. The system was called Advanced Photo System Classic Format. It failed after a few years but the format lives on as DX.

The 50mm lens is always only 50mm, regardless if on a DX or FX sensor. It is 50mm, period. That is why it is marked 50mm. 50mm is the only focal length it has.

A similar ratio was always true of different film sizes, but not until FX and DX digital were we able to use the same lens on different size sensors. So this becomes a subject of discussion today.

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We fit lenses to cameras based on the diagonal measure of the rectangular format. As an example, the full frame format measures 24mm height by 36mm length. The diagonal measure of this rectangle is 45mm. If we mount a 45mm lens, the view delivered is said to be “normal”, meaning the delivered perspective will match the perspective delivered by our unaided eyes. In actual practice a 45mm lens is an offbeat value and by tradition we round this value up to 50mm. Stated differently, the industry standard for a “normal” lens mounted on full frame (FX) is 50mm. The DX format is 16mm height by 24mm length. The diagonal measure of this rectangle is 30mm. If we mount a 30mm lens on a DX camera, the delivered view is said to be “normal” as to perspective. The so called magnification factor or crop factor is determined by dividing the two diagonal measures. Thus 45mm ÷ 30mm = 1.5. The inverse of this value is 1/1.5 = 0.66. This tells us that the DX is 66% of the size of the FX.

Todays smaller digital sensors change things (cropped field of view from the smaller sensors). This smaller sensor requires shorter lenses now, to see the "same view width" that larger 35mm film always saw. So their experience no longer just knows (yet) on their new camera. So the point of this "effective focal length" thing is to compare, to tell users familiar with 35 mm film what a certain lens will do on their new cropped sensor. If we say this 50mm lens performs on DX just like we are used to 75 mm performing on 35 mm film (field of view wise), then this has meaning to them, they know what to expect from it. However, if you are not familiar with using 35 mm film, then effective focal length on 35 mm film is not likely a useful concept to you.

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In 1924 the Leica still camera was marketed by E. Leitz of Germany. This camera accepted 35mm movie film which was plentiful, a spin-off from the motion picture industry. Mr. O Barnack, chief Leitz engineer designed the Leica to be held mainly in a horizontal position. Thus with the format rotated 90⁰, he was able to double the 18mm height, making the frame width 36mm. The other dimension, the 24mm width became height.

Effective focal length is only about that other lens on that other sensor (35 mm film), only because that other 75 mm lens appears to have the same field of view on 35mm film (or FX is same size) as does the 50 mm lens on the DX sensor. The focal length on the DX sensor is 50 mm. Only that other lens is 75 mm, and if on that other larger sensor, it does have the same field of view as the 50mm on DX. We are speaking of two different lenses and two different sensors.

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I know that the effective focal length of the 50mm FX lens is actually 50 x 1.5 = 75mm, because I'm shooting with an APS-C sensor.

Not exactly. Not "incorrect", but you have to understand what it means. The 75mm will not be a useful number on DX. The 50mm lens is NOT 75mm, and there is no actual real thing called effective focal length. It is a purely hypothetical concept. Any lens (at any one zoom) only has one focal length, where it actually focuses light from infinity.

The focal length engraved on the lens is the actual focal length. This actual focal length multiplied by the crop or magnification factor can be used by us “gray hairs” who are familiar with 35mm cameras. The crop factor is likely useless to those who never worked with a full frame.

As to how we use the crop factor: We “gray hairs” are super familiar with full frame 35mm cameras. The 35mm part of the name is derived from the width of the roll film they accept. Thomas Edison made the first movie system. He built cameras and projection machines. Edison purchased long rolls of film from Kodak. The film was 70mm wide. Edison had the film slit down the middle making two rolls for the price of one. He needed the film punched along the edges to help transport the film in his movie camera. The width between the sprocket holes is 24mm. His move frame measured 24mm width by 18mm height. This size was used in the motion picture industry for many years.

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In any DLSR, regardles of the crop factor, it is expected to have some knoledge about the units, so you have a real phisical unit.

The point of this is that there are many people that used 35mm film for years or decades. They are very used to exactly what a 50 or 75 mm lens will see and do, on 35 mm film. Their experience just knows.

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2) In some cellphones, the phisical size of the elements is so tiny, that saying "the camera has a 8mm focal length" could make someone think "Oh I have a super wide lens" which is not the case. Therefore manufacturers use the 35mm equivalent.

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The Effective focal length published with lenses for smaller sensors always compares to 35 mm film size (which is same as FX size, called Full Frame). However, we can compare the field of view of any two sensor sizes. For example, imagine 1/2 inch and 2 inch sensors (film maybe). The larger one is 4x larger than the smaller, so the crop factor is 4x, and (with the same lens) the larger one will have a field of view 4x wider than the smaller, and will need an effective focal length 4x longer to see the same reduced field of view as the smaller one. Different sensors can be different shapes (3:2, 4:3, 16:9) so crop factor actually compares diagonal of the frames.

What I'm curious to know is: when I purchased the 35mm DX lens, is that truly a 35mm length or is it 35 x 1.5 = 52.5mm? In other words, when I use a DX lens must I still do the same crop factor calculation as when I use an FX series lens? Would a 35mm FX lens on a full-frame camera "be the same" as a 35mm DX lens on an APS-C camera?

1) From history the most popular format was the 35mm film. That is still the main reference, so you sort of know the final result. That is why you offent want to find a equivalent. But that is a different matter.

If you were to use the more expense FF version of the 35mm lens on a DX camera, it would look the same (apart of course for differences due to lens quality) as the DX lens on the DX body.