DOF change when keeping subject size same in the frame

Question

What I have heard is you get more background blur (narrow DoF) with lenses with longer focal lengths. And another thing to get narrow DOF is the distance between the subject and the sensor, the lesser the distance the narrower the DoF. So if I use two lenses 50mm f1.4 and 85mm f1.4 to shoot a headshot, to keep the subject size same on the frame, with 85mm I will have to back off a little bit, so in that case with 85mm lens I'll get less background blur since the distance between the sensor and the subject increased?

I have looked at the suggested answers to What exactly determines depth of field?, but what I don't understand is that with 85mm lens, I have to back off to keep the same subject size, and that increases the subject to sensor distance, but how does the 85mm gives more background blur?

And also since aperture and sensor size is equivalent in both cases (by looking at the factors that affects DOF), only the other two factors - subject distance and focal length - should be the determining factors here. So does that mean the effect from longer focal length (85mm vs 50mm) is greater towards narrow DOF, than the subject distance?

Answer 1

Longer focal length lenses have shallower depth of field (DoF) than shorter focal length lenses if both are set to the same f-number when both are used at the same subject distance.

On the other hand, for the same lens and aperture setting a longer subject distance increases the DoF.

In the case of changing the shooting distance to maintain the same subject size in the frame the two factors at play here more or less offset each other fairly equally. Exactly how equal depends on how close or far the subject is with the base lens and shooting distance.

The following assumes an APS-C camera with a crop factor of 1.6X and a standard viewing condition of an 8x10 print viewed at 12 inches by a person with 20/20 vision.

If we use a 50mm lens set at f/1.4 at a distance of 10 feet we get a DoF of about 0.65 feet (7.8 inches). Roughly half of the DoF is in front of the focus distance and the other half is behind it.

If we use an 85mm lens set at f/1.4 at a distance of 10 feet we get a DoF of only about 0.22 feet (2.64 inches)! That is roughly 1/3 the DoF of the 50mm lens. But the subject will be 1.7X as large in the photo due to the difference in focal length.

So we then back up to 17 feet to make the subject the same size in the frame with the 85mm lens that it was in the frame at 10 feet with the 50mm lens.

If we use an 85mm lens set at f/1.4 at a distance of 17 feet we get a DoF of about 0.64 feet (7.68 inches), also fairly evenly split between in front of and behind the focus distance. We're not quite back to the 0.65 feet we got with the 50mm lens at 10 feet, but we're within 1.5% or so.

As the focus distance increases so does the difference between the two lenses when framing the same subject the same size.
50mm f/1.4 at 100 feet gives 73 feet DoF distributed 1:2 in front of and behind the focus distance. 85mm f/1.4 at 170 feet gives 68 feet DoF distributed 2:3 in front of and behind the focus distance.

This more or less continues until the shorter 50mm lens reaches hyperfocal distance at about 305 feet while the longer 85mm lens doesn't reach hyperfocal distance until 882 feet. Since any focus distance past 305 feet gives the 50mm lens infinite DoF (most of it behind the point of focus), it will have greater DoF than the 85mm lens at distances between 518 feet and 882 feet.

What is interesting is that the amount of DoF in front of the lens at 400 feet with the 50mm lens is about 227 feet. The amount of DoF in front of the 85mm lens at 680 feet (to frame the subject the same size) is 296 feet. So even though the 50mm lens at 400 feet has more DoF behind the subject, the 85mm lens at 680 feet (to keep the subject the same size) has more DoF in front of the subject.

In the real world, the resolution differences between the 85mm and the 50mm lenses will probably affect the perceived DoF more at these longer distances than the differences in theoretical calculated DoF.

Answer 2

The span of DOF depends on the tolerable diameter of the image disks that comprise the picture. All lenses image by projecting an image made up of a googolplex of tiny image discs. It is the size of these circles that dictates how the image will appear as to sharpness and the span of DOF.

These image circles overlap with indistinct bounders. They are called circles of confusion. Is the image sharp? This is a subjective call however the agreed upon standards are circles of confusion viewed from a distance equal to or greater than 1000 diameters. This works out to a circle 0.5mm in diameter viewed from 500mm (1/50 inch viewed at 20 inches). Technically that’s 3.4 minutes of arc or smaller.

Key to this discussion: A pin-hole camera has a super tiny aperture diameter. The image cast by the pin-hole has limitless DOF. Everything is rendered with equal sharpness regardless of camera to subject distance. It’s the tiny working diameter of the aperture that does the trick. Now the f/number is computed by dividing the focal length by the working diameter.

The 50mm with the aperture set to f/1.4, has a working diameter is 50 ÷ 1.4 = 35.7mm working diameter.

The 85mm set to f/1.4, the working diameter is 85 ÷ 1.4 = 60.7mm working diameter.

The larger the working diameter the larger the image circles the narrower the span of DOF.

Depth-of-field is key controlling factors

1. f/number (working aperture diameter)

2. focal length

3. subject distance

4. magnification applied to yield the observed image

5. distance to the observed image

6. acuity of eyesight of observer

7. subjective assessment of sharpness

Answer 3

For the EDIT: that's since 50mm and 85mm lenses are optically different. The DOF is part of the characteristics of the lens.

A longer lens compresses the image more, notice the difference in the background when you keep the subject the same size in the frame . That's compression, due to the compression the DOF gets smaller. That's why when shooting with wide angle lenses it is hard to get that blurry background.

I hope this helps : )