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I am reading some material on resolving power of lens and diffraction effect. As I known, the first on who consider the relation of diffraction and resolution is E. Abbe in 1873, who gave the following relation

[tex]\sin\alpha = \lambda / (2 n D)[/tex]

where n is the index of refracion and D is aperature diameter. However, in the text of optics, I found something similar but different

[tex]\sin\alpha = 1.22 \lambda / D[/tex]

so what's the difference between these? How does the 1.22 come from?

BTW, later in the text, I also read a criterion call Rayleigh's criterion which just approximate [tex]\sin\alpha[/tex] as [tex]\alpha[/tex] (I guess), so does Rayleigh's criterion only an approximation of Abbe's expression?