Do you get more bokeh on a APSC sensor with a full frame 50mm f/1.8 lens or a APSC 30mm f/1.4?

The Sigma 56mm f/1.4 would have the most background blur of the three, but the Sigma 30mm f/1.4 is very close because you need to move much closer for the same framing. The Minolta 50mm f/1.8 will have more depth of field, and not as much background blur as the other two.

The type of lens or "native" mount does not matter. All that matters is the camera format used, the aperture used, the actual focal length of the lens, and the shooting distance. Find yourself an online Magnification calculator, and Depth of Field calculator, and you can run some numbers yourself.

In general "Faster" lenses have less depth of field than slower lenses provided you are shooting them wide open.

Longer lenses tend to have less depth of field, but in order to get the same framing for each photo, you will have to move closer with the shorter lenses. Because you need to move closer with shorter lenses, the differences tend to be cancelled out.

The size of the eye you are looking out is f/a where a is the aperture number. That's independent from crop factor. So you have 30mm/1.4, 50mm/1.8, 56mm/1.4 and the latter clearly is the largest. So at equal distance, the background will be most separated with the last lens. Of course, you would not use those lenses at equal distance if you aim for the same framing.

At equal framing, your object distance will be proportional to the focal length, so the geometry of the cone from entrance pupil to a point in the subject plane, given equal framing, only depends on the aperture number. The cone sections of this cone determine the size of bokeh circles in the world. However, the world makes it into the camera by perspective, and with a shorter distance, objects grow faster in the foreground and shrink faster in the background. So for best background blur, you want the bokeh circles to appear larger and would choose a focal length that does not let the background shrink as much.

In other words: 56mm/1.4 clearly is the bokeh winner for background bokeh, even though at equal framing the 30mm/1.4 lens will be better at dissolving foreground objects (like when shooting through a thicket or fence that is still in reach, given your desired subject framing).

Depth of Field is computed from focal length, aperture, focus distance, and also sensor size. The distance limit of the depth of field is where the blur circle diameter is computed to exceed the maximum acceptable Circle of Confusion, which is computed from sensor diagonal size.

With all other factors equal:

A shorter focal length has greater depth of field than a longer focal length.

A stopped down aperture has greater depth of field than a more open aperture.

A greater focus distance has greater depth of field than a shorter distance.

The CoC computed for a smaller APS sensor has LESS DOF than a larger sensor, because (like tiny film) a smaller sensor is a smaller image which must be enlarged more to the final viewing size, and enlargement is detrimental to apparent depth of field. We recognize blur much easier when enlarged more. Sensor size is definitely a factor of Depth of Field.

However, a large offsetting factor is that the smaller sensor ordinarily must use a shorter lens to see the same normal field of view as the larger sensor, which becomes a greater factor (computing DOF squares focal length, but the other terms are not squared). So typically in practice, small senors with their necessary shorter lens see more DOF than larger sensors with their longer lens.

Any Depth of Field calculator will give the DOF numbers. My site offers one at https://www.scantips.com/lights/dof.html that will also compute the blur circle diameter at some specified background distance. It promotes the standard idea that a longer lens standing back with perhaps a f/4 lens can offer greater background blurring than a shorter lens standing closer with a f/1.8 lens (yet with greater DOF AT THE SUBJECT, and doesn't otherwise suffer the f/1.8 aberrations).

I'm going to chime in with a far less precise response (credit to the previous responders). You asked which setup would provide "more" bokeh. As I'm sure you know, bokeh in all its facets - the 'amount', the shape of the background objects (circular, angular etc) - is one of the most subject aspects of photography. It is so much more than blur. That definitely applies to being able to quantify it; there is no real way to do so.

What I can say is this: assuming correct framing, composition and focus, you're going to have 'a lot' of bokeh either at f-1.4 or f-1.8 for focal lengths ranging from appx 35mm-200mm. The deciding factor has to be which one do you prefer the look of. There are some lenses which have been engineered specifically to generate "beautiful" bokeh and in certain cases this is true. The soon-to-be-delivered Nikon Nocte 58m f-0.95 will likely be one of them, the Zeiss Otus 55mm f-1.4 is another although the latter is also supernaturally sharp (both are full frame). However these are both multi thousand dollar lenses and thus not available to most of us. If you have access to lens rental that's an obvious approach but I'm guessing that may not be the case. To be honest, the greatest importance of having a f-1.4 vs f-1.8 is the extra light. If I had to make your specific decision, I'd opt for the f-1.8 simply because that's what I use and the bokeh is lovely.

Of course if one wants to really go for it, you can take the approach Stanley Kubrick took when filming "Barry Lyndon". He had a scene lit by only three candles and did not want any artificial light. He therefore procured a f-0.7 from NASA although it was a bummer for the actors who had to move in a perfectly lateral manner given how razor thin the DOF was. But I digress now...

(More of a qualitative answer, I appreciate but I hope the perspective can be helpful).

To approximate amount of blur across lenses using the same sensor format, calculate focal length/aperture. This gives the aperture size, which directly correlates with the amount of blur produced in resulting images. Higher numbers ⇒ more background blur.

• 30/1.4 = 21.43
• 50/1.8 = 27.78
• 56/1.4 = 40

From this, we can see that the 50/1.8 lens will have a bit more blur than the 30/1.4 when used wide open. The 56/1.4 lens will have much more blur than either of the others.

Note: Depth of field is different from bokeh, which is different from amount of blur. DOF is specifically about the region that is within acceptable focus given specified viewing conditions. It is possible to have narrow DOF while having only a small amount of blur in out-of-focus areas.