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I am trying to figure out an equivalent telephoto lens to the newer periscope cameras that report focal lengths in 35 mm equivalents. There are some similar threads such as How do I convert lens focal length (mm) to x-times optical zoom? but they don't answer this specific question.

My P30pro and P50pro pictures state a number such as 1000 mm or 1600 mm equivalent focal length. How does that compare to say a Sony a6000 with a 55-210 mm lens?

On a related note, can anyone recommend a starter telephoto lens and mirrorless camera that can take equivalent photos?

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The photo industry has selected the full frame 35mm camera to be the benchmark. The 35mm film camera has been around for over 100 years. This camera produces an image on 35mm wide photo film. This film was generated for the motion picture industry. It features sprocket holes along both edges which served to steadily transport film smoothly through a movie camera and projector. The sprocket holes prevent the use of the entire 35mm wide film strip. The usable space between sprocket holes is 24mm. The 35mm still camera produced a negative or slide image that measures 36mm wide by 24mm high. The diagonal (corner-to-corner) measure is 43.3mm. The diagonal measure of this image is the key to the question you are asking.

As technology advances, the frame (image) size produced by the camera naturally decreases. This is because ways are discovered that allow smaller cameras with little impairment to image quality. As an example, the next step-down is the APS-C format, it measures 24mm wide by 16mm high with a diagonal of 29mm.

Now lenses for cameras are characterized by their focal length. This is a measurement taken, from a cardinal point called the rear nodal to the focused image when the camera is imaging a far distant object (like a star). This focal length value is generally expressed in millimeters. It technically conveys the power of the lens (size of images of objects). Additionally, the focal length together with the format size permits the angle of view, as seen by the camera, to be computed. If you were to mount a lens with a focal length identical to the diagonal measure of the format, the angle of view will be 53°. If the format is the classic rectangular shape, the horizonal angle of view is likely 45°. Such a lash up is generally termed “normal” for focal length. Shorter focal lengths yield wide-angle views whereas longer focal lengths produce a telephoto (magnified view).

Since the 35mm format is the benchmark, a useful way to make a comparison is by computing what is called the “crop factor” or “magnification factor”. We divide the two formats' diagonal measure to obtain this value. To compare the 35mm full frame with the APS-C we divide 43.3 ÷ 29 =1.5 (rounded). What does this 1.5 crop factor reveal? If a 50mm is mounted on a 35mm camera, mount a 50 ÷ 1.5 = 35 (rounded) on an APS-C and you will have a lash-up that delivers the same angle of view.

If a 1000mm telephoto is mounted on a 35mm camera, what focal length mounted on an APS-C delivers a comparable angle of view? Answer 1000 ÷ 1.5 = 600 (rounded).

Find out the frame size of your camera, compute the diagonal and divide into 43mm to find your crop / magnification factor.

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There are multiple ways that "equivalent" can be interpreted, but what you are probably* thinking of as equivalent is a camera/lens combination that captures the same angle of view as your phone photos. I'm not sure if your phone is using "digital" zoom, but assuming not, then if a photo reports an equivalent focal length of 1000 mm, then what you want is a camera/lens combination that also has an "equivalent focal length" of 1000 mm. That kind of lens for a large-sensor camera doesn't come cheap.

There are other ways of getting an "equivalent" image, e.g. shooting with a lens that captures a wider angle of view, and then simply cropping your result. (This is in fact where the whole concept around "equivalent focal length" came from – when crop sensor cameras appeared, allowing existing full-frame lenses to be mounted.) With a larger sensor, a good lens and good technique, you can get much better results this way, even if the equivalent focal length doesn't match exactly.

Just by way of example lenses and prices:

In a comment you mention the Sony α6000. Since this is an APS-C camera, with a 1.5x "crop factor", then mounting, for example, Sony's 200-600mm lens would give you an equivalent focal length range of 300-900mm (but with a larger sensor and better lens than your phone has).

* maybe not

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It's not the focal length that matters. It's the lens resolution.

Generally lenses used with small sensors have poor optical quality. I have taken picture of the moon with 400mm on a full frame camera (EOS RP) and 55-250mm on a crop sensor camera (EOS 2000D).

Here's the 250mm shot on a crop sensor camera (EOS 2000D + 55-250mm f/4-5.6 IS STM):

moon 250mm crop sensor

Here's the 400mm shot on a full frame camera (EOS RP + EF 400mm f/5.6):

moon 400mm full frame

As you can see, the more expensive full frame lens has higher optical quality. The quality of the camera sensor doesn't matter here, they're about the same megapixel count. Both 250mm on crop sensor and 400mm on full frame have the same 35mm effective focal length (400mm).

Generally for full frame mirrorless cameras, you don't use longer lenses than about 800mm. I'm confident that a RF 800mm f/11 lens for example would be of much better quality than any "periscope camera" with 1600mm equivalent focal length.

Some lenses to consider at around ~1000 USD (for Canon cameras, EF or RF):

  • Canon EF 400mm f/5.6 (only available used, discontinued)
  • Tamron EF 100mm-400mm f/4.5-6.3
  • Canon RF 800mm f/11
  • Canon RF 100mm-400mm f/5.6-8

As for the mirrorless camera, if you want to take pictures of objects far away you might want to wait until Canon releases its crop sensor RF mirrorless cameras. EOS M is a dead end and the full frame cameras are usually more expensive than crop sensor cameras and not as good for telephoto photography.

I'm sure some Nikon or Sony user can recommend lenses for Nikon or Sony mirrorless cameras.

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    AIUI, the zoom lens will always be a slightly lower quality than a fixed lens of equal length, so this is, in that respect, a somewhat unfair comparison.
    – FreeMan
    May 20, 2022 at 14:50
  • @FreeMan That's one factor but another factor is that the better lens cost 6x more as new when you could still buy it. A less expensive lens will always be a slightly lower quality than a more expensive lens of equal length...
    – juhist
    May 20, 2022 at 16:13

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