Back then, we knew what a 24 mm view did before, but it becomes something different on DX. Log-log graphs of focal length vs crop factor vs diagonal, horizontal and vertical angles of view for film or sensors of 3:2 and 4:3 aspect ratios by CMG Lee. In the film days, medium size roll film, and view camera sheet film, were very different sizes than 35 mm film, which again required lenses with different focal lengths to be used (to get the same normal viewing angle). Crop Factor is the ratio of the two sensor sizes, ratio equal to larger/smaller. The basic fact is that cropping an image with a smaller sensor can only show a smaller Field of View, but it cannot affect what the lens does. The meaning of this is that a full frame camera sensor is 1.5x larger, and if standing in the same place, and both used the same lens focal length, then the larger sensor would see field of view 1.5x larger (because the smaller sensor "crops" the view). Crop Factor is about the The Equivalent Focal Length applies to the 35 mm film camera frame.But the Equivalent Focal Length lens is mounted on the OTHER full size sensor, Not on the cropped camera.Digital Crop Factor today is arbitrarily referenced to the 35 mm film diagonal, the size of 35 mm diagonal / size of sensor diagonal.The cropped camera of course uses its actual real focal length.

The "Equivalent" term just means this is the "Equivalent" But (at same enlargement), the DX image is actually this relative size. OK, yes, of course the ratio calculation can be reversed to show the equivalent view that THIS camera would see, as compared to this same lens on the full size sensor camera (and the third calculator below will do that). The yellow line shows an example where 18 mm on 3:2 general APS-C is equivalent to 27 mm and yields a vertical angle of 48 degrees.

Any lens can only do whatever its focal length does do. When you can believe that, then you've got it. Otherwise, if full frame is of no concern, then it would seem that neither should crop factor be.
But instead, if the focal lengths used are adjusted to be the Equivalent relationship (instead on a full frame sensor that uses the longer lens with equivalent focal length multiplied by the crop factor of the smaller sensor), it is possible to make the Field of View be Equivalent. The cropped sensor simply captures a smaller cropped image. If the customer does not have a full frame camera say an APS-C or MFT instead, use the chart below:So an 80mm Hassy lens is going to give a similar angle of view to a 205mm lens when on a APS-C camera.
And it is shown enlarged 1.5x more here, so that the cropped DX frame comes out the same size as the FX size. FWIW, a typical compact camera with a tiny 7x5 mm sensor and shooting with maybe a 9 mm lens does even more of this, with a crop factor maybe 5 to 1 compared to 35 mm film FX size. A 200 mm lens on Full Frame acts like 200 mm, in comparison to 35 mm film. A Crop Factor of 1.5 means that (if both are using the same lens with same focal length) the larger Full Frame sensor sees a Field of View 1.5x larger dimensions than the small sensor (orange sensor case in diagram). Sports and wildlife photographers may prefer the DSLR 1.5x crop camera (over full frame) because its smaller cropped area makes their lens appear 1.5x longer (only as compared to using that Equivalent focal length on a full frame sensor, like 35 mm film).

Equivalent focal length only applies to the field of view that a 35 mm film frame would see.

By an odd coincidence the 4x5 focusing panel is marked for smaller formats so framing for them with it … 36mm / 24mm = 1.5x for APS-C). This smaller image from the smaller cropped view of the smaller sensor, The normal way it is always seen published compares the field of view of the smaller sensor to a 35 mm film camera (called 1x full frame) with its longer Equivalent Focal Length to see the same field of view. And it does, they may not have to buy a new lens. The full frame camera sees a 1.5x or 1.6x wider view than the 1.5x or 1.6x cropped sensor.

6 x 9 Crop Factor = 0.43. 80 * 1.6 = 128 * 1.6 = 204.8 ~ 205mm Or of course, we can always crop FX to the DX view and size anytime later. You can find information on the sensor size in your camera in the manual, product information of the manufacturer of on DPReview.com. The same lens of course projects the same image on the two sensors. DX is a smaller sensor, and this "crop" changes the viewed area, which causes the differences between FX vs. DX.

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