When the foreground of the scene is further away than the hyperfocal (as in the case presented in the question), focus on the foreground, as a result the whole scene will be in focus.
In fact, any focusing distance greater than the hyperfocal will get, in this case, the whole scene in focus. Focus on the foreground, as proposed above, is simply practical. And it seems to me that this is what a camera does in autofocus auto mode (i.e. when you let it choose where to focus) at least for the less sophisticated camera.
The explanations that follow are a little long but allow to come back to certain points that must be perfectly assimilated. The most important of these point is the two definitions of sharpness.
I. Shapness / Sharpness Range - Depth of Field / Hyperfocal
There are two possible approaches to the sharpness in digital photography:
- getting the best possible sharpness given the sensor
- adequate sharpness when the image is viewed
The first approach (hereinafter referred to as "digital") leads to take into account the size of the sensor sites.
The second is the legacy approach (hereinafter referred a bit misleadingly to as "film") , but it is still relevant for digital photography, as the view of humans has not evolved. Indeed, this definition of sharpness is based on the human visual acuity. As the eye has a limited power of resolution, any spot on the reproduced image (printout or screen) whose size is smaller than what the visual acuity can distinguish is interpreted as a point.
The size of this spot on the reproduced image corresponds to the diameter of a circle on the sensor (or film), this diameter is what is called "circle of confusion".
Obviously when, as can be done on a screen (pixel peeping), the image is enlarged, the assumption taken for the calculation of the circle of confusion is no longer valid.
It is therefore very important to determine what the objective is in terms of sharpness digital or film.
b. Sharpness Range - Depth of Field
When my focus is made at a distance D, some of the points located in front will result on the sensor by a spot whose size is smaller than the confuge circle, these points will appear sharp. The smallest distance for which these points appear sharp corresponds to the first sharpness plane. In the following, the distance to this plane is noted FSP.
Reciprocally, the last sharpness plane (LSP) corresponds to the distance beyond which the points will start to appear unsharp.In the following, the distance to this plane is noted LSP.
The space between these two planes (or the range of distances between these two planes) is the sharpness range also called "depth of field".
But remember, there are two notions of sharpness, therefore two notions of depth of field.
When a lens has depth-of-field markers, these markers are positioned taking into account "film sharpness".
By the way, some camera that indicate a depth of field scale in the viewfinder allow to choose on which of the two sharpness (digital ou film) notions the scale should be based.
There are formulas to determine FSP and LSP but the simplest call for the hyperfocal distance.
c. Hyperfocal distance
Note: the following is applicable to the common case (i.e. outside of macro photography) when the distance of the scene is much greater than the focal length.
The hyperfocal distance (H) is defined as the shortest focusing distance for which points at infinity remain sharp.
This distance is given by the formula H = f² / (N c) in which f si the focal length, N the f stop number, c the value of the circle of confusion.
With the hyperfocal, the formulas for FSP et LSP are FSP = D H / (H + D) and LSP = D H / (H - D) in which D is the focus distance.
Applying thess formulas, we find that for D = H then LSP = infinity, which is reassuring since this is how the hyperfocal; and also that FSP = H/2. Thus, by focusing at the distance of the hyperfocal, all the points whose distance is between half the hyperfocal and infinity are sharp. We can also see that for an focus at infinity, FSP = H which is just as interesting. It is also the second definition for the hyperfocal.
But again, remember that there are two notions of sharpness, therefore two notions of hyperfocal.
Reformulation the question
From the above, it is obvious that if the foreground of the scene is at a distance greater than the hyperfocal, any focusing distance between the hyperfocal and infinity will ensure sharpness at any point of the scene.
It is however interesting to reformulate the question as follows "For an aperture N, a focal length f, a scene in which the first plane is at the distance d1 and the last plane at the distance d2 (possibly infinity), at what distance D must the focus be made to ensure the best sharpness?"
To keep it short, D = 2 (d1 d2) / (d1 + d2), which gives for d2 = infinity, D = 2 d1.
However, the above does not take into account defects of the lens, nor especially the nature of the light which introduces diffraction. Simply put, when light passes through a hole, it spreads beyond this hole, the more as the hole is smaller.
Given the data provided (24mm, f/11, H:5'8''), we can deduce that you are using a full format camera. With an aperture of f/11, your image will be affected by diffraction if your sensor has more than 24M pixels.
As a rule of thumb , the "sweet pot" of sullframe lenses is around f/8.
So what I would suggest in the case described in the original question is:
- set the aperture (f/8)
- for verification, compute the corresponding hyperfocal for an aperture of one stop down (f/5.6): 11' 4 "
- focus at 10 000 feets