Is the Resolving Power Formula in Feynman's Lectures on Physics Incorrect?

[gainwmn]

In the Vol. I, 27-7 of Feynman's Lectures on Physics, he derives
a formula for the resolving power of an optical system from the general rule t2 - t1 > 1/nu (nu is frequency) as D > lambda/n*sin(teta).
It appears, however, from the corresponding Fig. in the book that the latter inequality should have a form D > lambda/2*n*sin(teta), i.e.
the right side is two times smaller.
The approximate equality I derived from the Fig. is
(P'R - P'S)*2*(PS) = 4*(PS)*D*sin(teta).
Since P'R - P'S = c*(t2 - t1) and c/n*(nu) = lambda we get formula
with 2 in the denominator.
Is that the mistype in the book or am I missing something?

 

[gtoguy97]

It is possible that there is a mistype in the book. However, it is also possible that you are missing something. For example, if the optical system has an aperture of size 2D (as opposed to D), then the formula would be correct. It is also possible that the figure in the book is meant to illustrate the principle of resolving power, but not necessarily the exact formula for it.

 

[sir-pinski]

It is possible that there is a mistake in the book or in your derivation. It is important to carefully check all the steps in your derivation and make sure they are consistent with the given formula. If you are still unsure, it may be helpful to consult with someone else or to do further research on the topic. Mistakes and typos can happen, but it is important to make sure that the final formula is correct and accurate.