The effect of crop sensors on lenses

Lenses used on crop-sensor cameras are a little different to those of full-frame cameras. Mostly this has to do with size – because the sensor is smaller, the image circle doesn’t need to be as large, and therefore less glass is needed in their construction. This allows crop-sensor lenses to be more compact, and lighter. The benefit is that for lenses like telephoto, a smaller size lens is required. A 300mm FF equivalent in MFT only needs to be 150mm. But what does focal-length equivalency mean?

Focal-Length Equivalency

The most visible effect of crop-sensors on lenses is the angle-of-view (AOV), which is essentially where the term crop comes from – the smaller sensor’s AOV is a crop of the full frame. Take a photograph with two cameras: one with a full-frame and another with an APS-C sensor, from the same position using lens with the same focal lengths. The camera with the APS-C sensor will have a more narrowed AOV. For example a 35mm lens on a FF camera has the same focal length as a FF on an MFT or APS-C camera, however the AOV will be different on each. An example of this is shown in Fig.1 for a 35mm lens (showing horizontal AOV).

Fig.1: AOV for 35mm lenses on FF, APS-C, and MFT

Now it should be made clear that none of this affects the focal length of the lens. The focal length of a lens remains the same – regardless of the sensor on the camera. Therefore a 50mm lens in FF, APS-C or MFT will always have a focal length of 50mm. What changes is the AOV of each of the lenses, and consequently the FOV. In order to obtain the same AOV on a cropped-sensor camera, a new lens with the appropriate focal length must be chosen.

Manufacturers of crop-sensors like to use the term “equivalent focal length“. Now this is the focal length AOV as it relates to full-frame. So Olympus says that a MFT lens with a focal length of 17mm has a 34mm FF equivalency. It has an AOV of 65° (diagonal, as per the lens specs), and a horizontal AOV of 54°. Here’s how we calculate those (21.64mm is the diagonal of the MFT sensor, which is 17.3×13mm in size):

  • 17mm MFT lens → 2*arctan(21.64/(2*17)) = 65° (diag)
  • 17mm MFT lens → 2*arctan(17.3/(2*17)) = 54° (hor)
  • 34mm FF lens → 2*arctan(36/(2*34)) = 55.8° (hor)

So a lens with a 17mm focal length on a camera with a 2.0× crop factor MFT sensor would give an AOV equivalent of to that of a 34mm lens. An APS-C sensor has a crop factor of ×1.5, so a 26mm lens would be required to give an AOV equivalent of the 34mm FF lens. Figure 2 depicts the differences between 50mm FF and APS-C lenses, and the similarities between a 50mm FF lens and a 35mm APS-C lens (which give approximately the same AOV/FOV).

Fig.2: Example of lens equivalencies: FF vs. APS-C (×1.5)

Interchangeability of Lenses

On a side note, FF lenses can be used on crop-sensor cameras because the image circle of the FF lens is larger than the crop sensor. The reverse is however not possible, as a CS lens has a smaller image circle than a FF sensor. The picture below illustrates the various combinations of FF/MFT sensor cameras, and FF/MFT lenses.

Fig.3:The effect of interchanging lenses between FF and crop sensor cameras.

Of course all this is pointless if you don’t care about comparing your crop-sensor camera to a full-frame camera.

NOTE: I tend to use horizontal AOV rather than the manufacturers more typical diagonal AOV. It makes more sense because I am generally viewing a scene in a horizontal context.

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