I am gonna compare APS-C and 24x36mm sensors.
For a lens projecting a rectilinear image (focused at infinity), the angle of view (α) can be calculated from the chosen dimension (d), and effective focal length (f) as follows:
d represents the size of the sensor (or film) in the measured direction.
For 35mm film which is 36 mm wide and 24mm high, d=36 mm must be used to obtain the horizontal angle of view and d=24 mm for the vertical angle.
For APS-C sensors, the size is 23.7 x 15.6mm. So, we can compute the angle with respect to the focal length and notice how it is nonlinear: a difference of 7mm at wide angle lens area between 9mm and 16mm yields 30° whereas a 7mm difference at tele lens area around 150mm doesn't lead to any perceptible variation in the angle.
Here is another more convenient representation, I found on the web, for 24x36mm sensors:
Now, 2 more convenient representations I did for APS-C sensors:
Let us see now, for APS-C sensors, what is the minimum shutter speed that can be used without tripod, flashes or image stabilization:
It's also nonlinear and we can see why it's not easy to use a tele-lens: shutter speed must be very fast for crisp images and the maximum aperture is usually smaller (f/2.8 max) than standard and wide angle lenses.
Let's now check the crisp area for different focusing distances and wide angle lenses, for APS-C sensor still. X axis stands for aperture (with vertical red line for common ones) and Y axis stands for the distance in meters: the lower curve models the closest distance for the crisp area and the upper one of the same color models the furthest crisp distance for a given focale length.
And now for standard lenses (tele-lenses have of course very narrow crisp area... very limited kinds of photographs):
Another way to appreciate the effect of focal length on depth of field is to analyze the hyperfocal focusing distance i.e. the focusing distance that will lead to crisp images from infinity to the closest distance. The dotted line stands for the hyperfocal distance and the plain line for the closest crisp distance:
Once again, large crisp area can be obtained with wide angle length.
Now, it's interesting to compare 24x36mm with APS-C sensors because there are not equivalent. Actually, if a 23mm focal length for an APS-C sensor is equivalent in terms of angle to a 35mm focal length lens for a 24x36mm sensor, the depth of field of the 23mm is the one you get with a 23mm lens, whatever the sensor is: it's an optical property. To make it easy, let's analyze separatly different focal lengths. There are 4 curves for each focal length. The upper left corner contains the hyperfocal distance and the closest crisp distance at hyperfocal. The upper right corner and lower curves contains the closest and furthest crisp distances for different aperture.
1) focal is 9mm. At aperture f/2.8 and focusing distance at 1m, the crisp area is 50cm → ∞
2) focal is 15mm. At aperture f/5.6 and focusing distance at 2m, the crisp area is 1m → ∞
3) focal is 21mm. At aperture f/8 and focusing distance at 1.5m, the crisp area is 1m → ∞
4) focal is 25mm. At aperture f/8 and focusing distance at 2m, the crisp area is 1.5m → 8m
5) focal is 28mm. At aperture f/8 and focusing distance at 3m, the crisp area is 2m → 8m
6) focal is 35mm.
7) focal is 50mm
8) focal is 90mm
I conclude that increasing the size of a camera sensor has limitation because of the optics. As we saw, it's easy to get narrow depth of field with a 50mm focal length and more. It's all the more easy that very large maximum aperture, close to f/1, use to be available for small sensors because lenses are smaller... What is difficult to obtain is large crisp area... A standard angle is 35mm for APS-C, 50mm for 24x36mm and 70mm for GFX medium format! Just remember the previous curves. The difficult question is not how to obtain bokeh but how to obtain crisp images. From that point of view, smaller sensors are much better... and smart-phone cameras perfectly adapted to capture crisp images...
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