To understand Rayleigh's criterion as applied to the pupil of the eye, notice that rays do not pass straight through the center of the lens system (cornea + lens) of the eye except at normal incidence because the indices of refraction on the two sides of the lens system are different. In a simplified model, suppose light from two point sources travels through air and passes through the pupil (diameter $a$ ). On the other side of the pupil, light travels through the vitreous fluid (index of refraction $n$ ). The figure shows two rays, one from each source, that pass through the center of the pupil. (a) What is the relationship between $\Delta \theta$, the angular separation of the two sources, and $\beta$, the angular separation of the two images? [Hint: Use Snell's law.] (b) The first diffraction minimum for light from source 1 occurs at angle $\phi$, where $a \sin \phi=1.22 \lambda$ [Eq. (25-13)]. Here, $\lambda$ is the wavelength in the vitreous fluid. According to Rayleigh's criterion, the sources can be resolved if the center of image 2 occurs no closer than the first diffraction minimum for
image 1 ; that is, if $\beta \geq \phi$ or, equivalently, $\sin \beta \geq \sin \phi$. Show that this is equivalent to Eq. ( $25-14$ ), where $\lambda_{0}$ is the wavelength in air.