Why are faster lenses sharper in the telephoto range?

Someone asked this question in a forum and here is a great answer that will be helpful to all of us!

“First off, lenses are designed for their specific maximum apertures. A 300mm f/4 is not a stopped down 300mm f/2.8. It was designed as a f/4 from its inception.

Virtually all lenses are sharpest at about two stops down from wide open. This is because lenses are designed for a range of apertures, and anything with any kind of range in its design must have compromises. The 300mm f/2.8, therefore, is sharpest at about f/5.6, and the 300mm f/4 at about f/8.

In theory, a lens could be designed with a single aperture and maximum sharpness at that aperture. Such a lens, however, would be severely limiting in its use. Mirror lenses have this drawback—this plus the fact that they are almost always use very poor glass to keep the price down.

Secondly, large aperture lenses require very primo front elements. These elements are the most critical elements in most lenses, and cannot tolerate aberations. After all, the light passes through these elements first, and, if distorted, remains distorted forever after. These elements are also the largest elements in the lenses. When grinding and polishing glass, the larger the diameter, the harder it is to prevent aberations from creeping in. Large aperture lenses means means super-precision grinding and polishing out to the very edges, which in turn means very high prices.

Take Canon’s 300mm “L” lenses as examples:
The EF 300mm f/2.8L IS USM has a front element with an active area about 107mm in diameter and sells for about $4340 at B&H.
The EF 300mm f/4L IS USM has a front element with an active area about 75mm in diameter and sells for about $1269 at B&H.

A lot of effort goes into that 32mm difference.”