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One of the lenses I have for my Nikon D3200 is the 50mm f/1.8 FX lens, which when placed on the DX sensor should act like a 75mm f/2.7.

On my Sony a6000, I have a 55-210mm f/4.5-6.3 lens made for the DX sensor.

However, when I take a carefully-framed picture with each camera and their respective lens, the Sony's FOV is narrower than the Nikon's.

Why?

Both are APS-C sensors, and the Sony is shooting at 50mm and the Nikon is shooting at [effectively] 75mm. The Nikon should be far more "zoomed in," but isn't.

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There is a general misunderstanding regarding sensors, lenses, and apparent zoom. The DX 3/2 zoom effect is misleading as nothing of the kind is actually happening.

50 mm is 50 mm, regardless of whether it's FX, DX, or large format.

A DX lens simply is not designed and built to have a high quality image or avoid vignetting over a larger area than the DX sensor, so it's cheaper and smaller to make. An FX lens provides good image over an area larger than the DX sensor, but that makes no difference whatsover on a DX as it's not seen.

The whole 3/2 zoom effect doesn't actually exist, the optics don't change. The perception comes about from cropping. A smaller sensor see less image. If you print or view this smaller crop area at the same size as a larger sensor, the result appears zoomed.

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  • Ah, so the crop-factor is really just saying that, for example, a 50mm lens on a full-frame camera would have to be replaced with a 75mm lens to have the same effective field-of-view as if you took that same 50mm lens and put it on a crop-sensor - but, as far as the crop-sensor is concerned, it's still 50mm (in terms of depth of field, etc) but would just have a smaller field-of-view? – iAdjunct Aug 20 '18 at 2:19
  • It is always still a 50 mm f/1.8 lens, but the 1.5x cropped sensor would see the same field of view that a full frame sensor would see with a 75 mm lens. Just meaning, on the smaller cropped sensor, it is a smaller cropped view. So it is called Equivalent focal length of 75 mm on a full full frame (35 mm film) camera (for users familiar with that, to know what it means). But it remains a 50 mm f/1.8 lens. The "Equivalent" 75 is on the full frame sensor, NOT on the cropped sensor. – WayneF Aug 20 '18 at 2:43
  • Does this also mean that if my 50mm lens was F1.8, then a full-frame camera would need a 75mm F4.0 lens to have the same picture and same effective light collection (taking into account the larger sensor area) to achieve the same picture? (Theoretically, the 75mm F4.0 would require the FX to have the same ISO, shutter-speed, etc at F4.0 as the DX would with its 50mm F1.8 lens). – iAdjunct Aug 20 '18 at 3:12
  • Exposure is determined by shutter speed, aperture, ISO. Change any one, and at least one of the others needs to change to compensate. To get the "same" look, as 50/1.8 on a crop sensor, you could use 75/2.7 on a full frame. However, because of the aperture change, shutter speed or ISO would also need to change. – xiota Aug 20 '18 at 3:19
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    See this question for discussion of aperture f-stop and "same picture" equivalence. – Please Read My Profile Aug 20 '18 at 13:53
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You have two APS (DX) sensor cameras. Both have approximately the same size sensor. If you mount a 50mm lens on either, the angle of view will be the same.

You can duplicate this angle of view on an FX (full frame) if you mount a 75mm lens

Your Sony a600 sports a 55-210 zoom lens. It will not reach 50mm, thus it delivers a slightly narrower angle of view then the Nikon D3200 with a 50mm lens mounted. If you were to mount a 55mm on Nikon D3200, then it would deliver the same angle of view as the Sony set to 55mm.

As to the 75mm -- We are talking about depth-of-field and image size differences between the FX vs a DX. Suppose you mount a 50mm on DX and compose this scene. You will have established a specific camera-to-subject distance to achieve the boundaries you desire.

Now you attempt to duplicate this scene with its boundaries using a FX. You will discover that if you mount a 50mm on a FX, you must move in closer to keep the same boundaries. This is because the FX sensor is larger, thus it sees a wider angle of view.

To duplicate the same boundaries with FX at the same subject distance, you must mount a 75mm. OK now the compositions are the same but the depth-of-fields are different. This is because one of the many components of depth-of-field is subject distance. Now to approximately duplicate the depth-of-fields, you must stop down the lens on the FX. This is why the 75mm will be set to f/2.7 and the DX set to f/1.8. Such settings duplicate the depth-of-field at different subject distances.

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  • DX is crop body. FX is full frame. – Michael C Aug 20 '18 at 10:24
  • Tip of the hat to Michael Clark for making this correction. – Alan Marcus Aug 20 '18 at 13:53
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You appear to be confusing the actual focal length with "equivalent" focal length. Equivalent focal length is the focal length that would be required to get the same field of view on a full-frame sensor. Equivalent focal length is used to compare compositional possibilities with lenses across different sensor sizes.

  • The 50mm F1.8 FX lens is still a 50mm F1.8 lens on a crop sensor. You are simply capturing a smaller area than you would on a full-frame sensor. (It is cropping.)

  • The 55-210mm F4.5-6.3 lens is still be a 55-210mm F4.5-6.3 on a full frame sensor. However, the imaging circle would be too small to cover the entire area of a full-frame sensor.

It can also be useful to multiply aperture by crop factor to get an idea of the effect sensor size will have on bokeh. However, people usually do not do this because exposure is not affected by sensor size.

Exposure is determined by shutter speed, aperture, ISO. Change any one, and at least one of the others needs to change to compensate.

  • To get the "same" look, as 50/1.8 on a crop sensor, you could use 75/2.7 on a full frame. However, because of the aperture change, shutter speed or ISO would also need to change.
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  • Thank you. When I'm talking about the different f-stops, I'm taking into account two things: (1) The fact that the f-stop is a function of the aperture size (constant) and focal depth (which changes when we talk about the "equivalent" focal depth); and (2) the fact that the FX sensor is bigger, so when we talk about a lens for the FX camera to get the same picture, the focal length is bigger and the F stop is lower. See me comments to the other answer as well. – iAdjunct Aug 20 '18 at 3:15
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    F-stop does not change when talking about "equivalent" focal length because "actual" focal length did not change. Equivalent focal length is used solely as a means to compare field of view. – xiota Aug 20 '18 at 3:22
  • There's no such thing as true equivalency. – Michael C Aug 20 '18 at 10:49
  • I didn't say there is no such thing as equivalent focal length. I said there's no such thing as true equivalency. For instance, if one alters the Av to maintain DoF, then the exposure is affected, so one must alter the Tv or the ISO to compensate. You can't take the same exact photo with two differently sized sensors. That's all explained in detail at the link. – Michael C Aug 20 '18 at 15:06
  • Actually, some users in this community have claimed such in the past. – Michael C Aug 20 '18 at 15:09
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Whether a lens is an FX or a DX lens, the actual focal length is always used. There are certain technical reasons why this is so, but the simplest is that a lens' focal length is defined as the distance from the film plane needed when the lens is focused at infinity to cast point light sources as a single point on the film plane. This doesn't change with regard to sensor size. What does change with regard to sensor size is the angle of view (AoV) or field of view (FoV) that a lens of a specific focal length will include in the part of the image circle that falls on the sensor.

What this means is that if you are using a 50mm lens on a Full Frame FX camera, the AoV will be about 46° diagonally. The same 50mm lens on a DX crop sensor body will have an AoV of about 31°. That is an equivalent AoV of about a 75mm lens on the FF body, and that is why camera manufacturers say that the 50mm lens on a crop body is a 75mm equivalent.¹ If you print photos taken of the same subject from the same distance using the same focal length lens with both a DX and FX camera on the same size paper, the image from the crop sensor camera will make the subject appear larger. This is because the ratio between the crop sensor size and the print size is greater than the ratio between the larger full frame sensor and the same print size, thus the magnification factor of the photo taken with the crop sensor body is higher when both are viewed at the same display size.

To understand the 35mm/FF equivalent FoV your 50mm and 55mm lenses yield on your D3200 and α6000, both lenses need to be multiplied by the crop factor, even though one of the lenses does not project a light circle large enough to fill a full frame sensor.

Both are APS-C sensors, and the Sony is shooting at 50mm and the Nikon is shooting at [effectively] 75mm. The Nikon should be far more "zoomed in," but isn't.

The Sony with the lens set at 55mm is shooting at [effectively] 82mm.

Your Nikon D3300 with 50mm FX lens is giving you the same angle of view that a 75mm lens will give on a full frame sensor. Your Sony α6000 is also giving you the same angle of view at 55mm that an 82mm lens would give on a full frame camera.

¹ There's no such thing as true equivalency when comparing disparately sized sensors. For a detailed discussion of this, please see this answer to Lens equivalent depth of field See also: Can a smaller sensor's "crop factor" be used to calculate the exact increase in depth of field?

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