7.6 Limits of resolution: the rayleigh criterion  (Page 3/6)

The answer in part (b) indicates that two stars separated by about half a light year can be resolved. The average distance between stars in a galaxy is on the order of 5 light years in the outer parts and about 1 light year near the galactic center. Therefore, the Hubble can resolve most of the individual stars in Andromeda galaxy, even though it lies at such a huge distance that its light takes 2 million years for its light to reach us. [link] shows another mirror used to observe radio waves from outer space.

Diffraction is not only a problem for optical instruments but also for the electromagnetic radiation itself. Any beam of light having a finite diameter $D$ and a wavelength $\lambda$ exhibits diffraction spreading. The beam spreads out with an angle $\theta$ given by the equation $\theta =1\text{.}\text{22}\frac{\lambda }{D}$ . Take, for example, a laser beam made of rays as parallel as possible (angles between rays as close to $\theta =\mathrm{0º}$ as possible) instead spreads out at an angle $\theta =1\text{.}\text{22}\lambda /D$ , where $D$ is the diameter of the beam and $\lambda$ is its wavelength. This spreading is impossible to observe for a flashlight, because its beam is not very parallel to start with. However, for long-distance transmission of laser beams or microwave signals, diffraction spreading can be significant (see [link] ). To avoid this, we can increase $D$ . This is done for laser light sent to the Moon to measure its distance from the Earth. The laser beam is expanded through a telescope to make $D$ much larger and $\theta$ smaller.

In most biology laboratories, resolution is presented when the use of the microscope is introduced. The ability of a lens to produce sharp images of two closely spaced point objects is called resolution. The smaller the distance $x$ by which two objects can be separated and still be seen as distinct, the greater the resolution. The resolving power of a lens is defined as that distance $x$ . An expression for resolving power is obtained from the Rayleigh criterion. In [link] (a) we have two point objects separated by a distance $x$ . According to the Rayleigh criterion, resolution is possible when the minimum angular separation is