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As Wikipedia says here
The smaller mirror used in APS-C cameras also allows optical elements to protrude further into the camera body, which enhances the possibilities for wide angle and very wide angle lenses, enabling them to be made smaller, lighter (containing less glass), faster (larger aperture) and less expensive.
How does a small mirror allow the possibilities for wide angle and very wide angle lenses to be enhanced by enabling them to be made containing less glass and larger apertures?
Just about any wide angle (WA) or ultra wide angle (UWA) lens used with an interchangeable lens camera will use a retrofocus design. That does mean larger, heavier, and more complex than a non-retrofocus design. But that doesn't mean all retrofocus lenses must be equally large and heavy (and expensive).
A wide angle lens that uses a retrofocus design is essentially a telephoto lens that has been turned around backwards. Have you ever looked the "wrong way" through a pair of binoculars? Instead of making everything bigger as is the case when looking through them correctly, everything is made smaller. That's what a retrofocus wide angle lens does.
Now compare the view looking the wrong way through an 8X power binocular compared to a 20X power binocular. When looking through them the wrong way the 20X power binocular will make things smaller than the 8X power binoculars. If both pair of binoculars are based on the same basic design and use the same types of materials, the 20X pair will be larger, heavier, and more expensive than the 8X pair.
So look at it this way - a 500mm telephoto lens has to be larger than a 300mm telephoto lens if each uses the same basic design (number, type, and arrangement of lens elements, materials with the same refractive index, etc.). Since WA and UWA retrofocus lenses are "backwards" telephoto lenses, the same is true of wide angle retrofocus lenses. With the same back focus distance an 8mm lens has to be "more retrofocus" than a 12mm lens which has to be "more retrofocus" than a 16mm lens and so on in much the same way that a 200mm lens has to be "more telephoto" than a 135mm lens which has to be "more telephoto" than an 85mm lens and so on.
That's why a 35mm f/2 lens is much easier and cheaper to design and make than a 24mm f/2 lens which is easier and cheaper to produce than a 14mm f/2 lens and so on. The corollary is that a reduction in the back focus distance allows a WA or UWA lens to be "less retro focal" than another lens with the same focal length but that requires a longer back focus distance.
It is not just a question of whether or not a lens must use a retrofocus design. It is also a question of just how much reverse telephoto power is required. Shorten the back focus distance for the same sensor size and a smaller reverse telephoto lens is required for the same angle of view/magnification factor.
The back focus distance is the distance between the back optical element of the lens and the film/sensor. This measurement is independent of the flange focal distance, sometime referred to as the registration distance. As long as there is nothing in the way the rearmost lens element can protrude into the camera and be closer to the film/sensor. With SLRs the first thing anything protruding into the lightbox would have a clearance issue with is the mirror. Even if the lens doesn't touch the mirror when it is all the way down, the mirror can strike the back of the lens when the mirror swings up out of the way to allow the film/sensor to be exposed by the opening of the shutter.
The advantage the smaller mirror gives is that it allows the back of the lens to be closer to the film/sensor without having clearance issues because the part of the mirror nearest to the lens will be further back in the camera and closer to the film/sensor than a larger mirror would.
The general advantage of allowing a short distance between the back of the lens and the sensor is that you don't need a retrofocus lens design. This is a lens design with additional elements forming an inverted telephoto arrangement to move the actual point of focus further away from the back of the lens. It is necessary to allow wide angle lenses on DSLRs. The difference between APS-C and 35mm framed DSLRs in relation to this is probably relatively small [as noted in a previous comment] but it is an area where there are real advantages for mirrorless cameras.
As an example the ratio of flange distances [distance from back of lens flange to sensor] for some typical lens mounts are 18mm for an ASPC mirrorless and 44mm for a DSLR. At focal lengths much less than this [lenses can protrude inside the flange distance] a retrofocal design is necessary. Of course an APSC camera requires a shorter focal length for the same field of view so the advantages are not quite as significant as the flange distance may indicate..
The main advantage of ASP-C compare to 35mm frame is simply that the coverage that the lens has to provide for the sensor is smaller. This means that all of the lens elements can be smaller in each dimension reducing the size and weight more than you might suspect from the ratio of sensor dimensions.
The focal length of a lens reveals its power. The APS-C, alias “compact digital” sports an imaging chip that is 66% of the size of the venerable “full frame” 35mm. The Dx sensor measures approximately 16mm height by 24mm length and the diagonal measure of this rectangle is 30mm.
Knowing the diagonal measure is important because it’s the value we use to determine the focal lengths that pertain to any particular format size. When we mount a lens with a focal length that matches the diagonal measure, this combination will deliver an angle of view of about 45° with the camera held horizontal (landscape) position. Often a diagonal angle of view is published; this will be 53°. This larger angle of view muddies the facts. It’s like the oddity of advertising a TV by its diagonal measure. Anyway, such a lash-up is labeled by the industry as a “normal” lens. In other word, “normal” translates to a view that about matches the human experience.
If we mount a lens that is shorter in focal length than the “normal”, the angle of view obtained increases. Thus the realm of wide-angle is attained when the mounted lens is 70% of “normal” or shorter. For the Fx, that’s 20mm or shorter. By the way, the realm of telephoto is 200% of normal or longer. Thus for the Fx, this is 60mm or longer.
Now the focal length is measurement taken from the lens to the image plane when the lens is imaging a far distant subject. We are talking about objects at infinity (symbol∞), “as far as the eye can see”. As we mount shorter and shorter lenses to gain a wider and wider angle of view, the rear element of the lens barrel gets ever closer to the image plane. Unless some special optical or mechanical design is implemented, the swinging mirror of the single lens reflex (SLR) design limits just how wide-angle we can go.
One countermeasure is to lock the mirror in the up position (picture taking position) this clears the way for a super short lens. The downside is, the SLR view through the lens is lost. This works, but most agree it’s far from satisfactory. Another solution is to design a wide-angle such that it resembles binoculars held wrong way around. This lash-up delivers a wide-angle view while maintaining an expanded back-focus distance that permits the reflex (to bend backwards) mirror to swing unimpeded. This lens design is called “retro-focus”. This works, but the lens maker is faced with heightened worries revolving around aberrations and distortions.
I actually think that the smaller reflex mirror of the Fx does not help because the smaller Fx format dictates that the focal lengths be shorter. Seems to me this will be proportional. In other words, the difficulties of the full frame are coequal to the difficulties of the Fx. In the end, the mirrorless design will win. The mirror design, absolutely needed for the film camera, can totally eliminate in the digital design. Once again, technology marches on.
The statement is simply false and there is no advantage.
What counts is not the specific distance but the proportion of distance to the other camera and lens dimensions. Assuming the same general design, when scaling the DSLR down from full frame to APS-C (or even further to smartphone camera size) nothing really changes geometrically (except for the amount of light).
What makes the difference is for example getting rid of the mirror, then, such mirrorless camera might use lens that cannot be used with a reflex camera.
