4.5 Circular apertures and resolution  (Page 3/8)

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 five light-years in the outer parts and about one 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 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 $\text{λ}$ exhibits diffraction spreading. The beam spreads out with an angle $\theta$ given by [link] , $\theta =1.22\lambda \text{/}D$ . Take, for example, a laser beam made of rays as parallel as possible (angles between rays as close to $\theta =0\text{°}$ as possible) instead spreads out at an angle $\theta =1.22\text{λ}\text{/}D$ , where D is the diameter of the beam and $\text{λ}$ 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 ( [link] ). To avoid this, we can increase D . This is done for laser light sent to the moon to measure its distance from Earth. The laser beam is expanded through a telescope to make D much larger and $\theta$ smaller.

In most biology laboratories, resolution is an issue when the use of the microscope is introduced. 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. [link] (a) shows two point objects separated by a distance x . According to the Rayleigh criterion, resolution is possible when the minimum angular separation is