"Moore's law is the observation that the number of transistors in a dense integrated circuit doubles about every two years." The law basically limits the improvement in the resolution of photolithography. Why should the resolution of photolithography follow such a pattern?
Let's take three facts and combine them:
- Chips are generated by photolithography
- The number of nodes per wafer follows Moore's law.
- The number of nodes increases, because the "size of a node" (more precise: critical dimension) gets smaller.
Assuming that "size of a node" is limited by the optical resolution of the photolithography machine (in fact a second limitation is often the sensitivity and selectivity of the photoresist) you get the answer to "Why does the resolution of photolithography follow Moore's law?".
Moore's law empirically tracked the development of 1) finer-resolution photoresists, 2) higher accuracy photomasking technology, 3) precision etching and metal-deposition technology, and 4) the development of ever-larger wafers.