Q. Is there a minimum shiur of rainbow that has to be seen in order to make the beracha or is any small amount enough (in length or in number of colors)?

A. Poskim disagree; Biur Halocho (229: 1) queries whether in order to recite a brocho on a rainbow one needs to see the full semicircle or even part of it is enough. Teshuvos Vehanhogos (O.H. 3: 76) rules that since Biur Halocho remains uncertain, as in every Sofek brocho (doubtful blessing) no brocho should be recited. Vezos Habrocho (p. 156) maintains that if only a small part is missing, a brocho can be recited.

However, other Poskim aver that even part of the rainbow is after all enough to bring to memory the established covenant and therefore suffices for a blessing (Chazon Ovadia p.473 quoting various other Poskim, Yalkut Yosef 3: 229:1, P’ninei Halocho p.227, Nesivei Halocho 229: 1)

Horav Shlomo Miller’s Shlit”a opinion is that if it shows the curvature of an arc, and as long as most people recognize it as a rainbow and call it so, one can recite a brocho over it.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a