This extract from a document I wrote on CCTV cameras might help you to understand it a bit better:
Imager size and choice of lens. The majority of domestic and industrial video cameras use one of two main sizes of imager. These are usually called the “One third inch” type and the “Quarter inch” type, and both are made in either B&W or colour versions. Other sizes are made, including larger “half inch” and “two-thirds-inch” types, but these are less common.
The active image size of a nominal “third Inch” imager is actually 4.8 x 3.6mm, while that of a nominal “quarter inch” imager is 3.6 x 2.7mm. You may have realized that the diagonal of a quarter inch 4:3 aspect ratio imager calculates to 4.5mm, whereas a quarter of an inch is actually 6.5mm. This is because the measurement convention is a carryover from old-fashioned thermionic camera tubes, where the size referred not the actual image area but to the diameter of the glass tube. Generally, the diagonal measurement of the usable sensor area of a camera tube was about two-thirds the physical diameter.
Modern lens sizing conventions. In the old days, CCTV cameras tended to have a quite short service life and were often replaced at frequent intervals. However the lenses did not usually wear out and, as good ones were expensive, normal practice was to fit the old lenses back onto new cameras with the same sized tubes. When CCD cameras became available, people naturally wished to continue with this practice but of course CCD cameras don’t have a “Tube”, so a range of CCDs was designed having pickup areas approximating the dimensions of the active pickup areas of common camera tube sizes.
So, a “half inch” CCD sensor actually meant: “One that can use a lens designed for a ‘half inch’ camera tube.” That all made perfect sense at the time, but in more recent years the system has gone completely off the rails.
First of all, while there are CCD and CMOS sensor sizes such as “third inch”, “quarter inch” and even “fifth inch” readily available, there have never actually been any “third inch”, “quarter inch” or “fifth inch” camera tubes! The smallest camera tubes ever made were “half inch”.
What these figures are now supposed to mean is that the actual diagonal of the pickup area of the image sensor is two-thirds the quoted dimension. So, a “one third inch” CCD or CMOS sensor actually has an active sensor diagonal measurement of 0.33 x 2/3 = 0.2 inches (about 5mm).
Even more bizarre is the current practice of quoting sensor sizes as nonsensical fractions such as “1/2.6 inch”. “1/2.6 inch” is actually intended to mean what it looks like it means: “1 inch ÷ 2.6” (= 0.385 inches). But the sensor diagonal size is only two-thirds this; about 0.25 inches or 6.5mm! Apart from the possible intention that “1/2.6 inch” sounds more impressive than “6.5mm”, it is hard to fathom the logic behind this system.
The true sensor diagonal in mm can be calculated by dividing 16.9 by the “decimal-ized divisor”.
So in the above example: 16.9 ÷ 2.6 = 6.5mm.
4/3 is the same as "1/0.75" and in that case the diagonal is 16.9 ÷ 0.75 = 22.6mm.