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Two pictures of the same galaxy taken by different telescopes are shown side by side. Photo a was taken with a ground-based telescope. It is quite blurry and black and white. Photo b was taken with the Hubble Space Telescope. It shows much more detail, including what looks like a gas cloud in front of the galaxy, and is in color.
These two photographs of the M82 galaxy give an idea of the observable detail using the Hubble Space Telescope compared with that using a ground-based telescope. (a) On the left is a ground-based image. (credit: Ricnun, Wikimedia Commons) (b) The photo on the right was captured by Hubble. (credit: NASA, ESA, and the Hubble Heritage Team (STScI/AURA))

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.

The figure shows a photograph from above looking into the Arecibo Telescope in Puerto Rico. It is a huge bowl-shaped structure lined with reflecting material. The diameter of the bowl is three times as long as a football field. Trees can be seen around the bowl, but they do not shade the bowl significantly.
A 305-m-diameter natural bowl at Arecibo in Puerto Rico is lined with reflective material, making it into a radio telescope. It is the largest curved focusing dish in the world. Although D size 12{D} {} for Arecibo is much larger than for the Hubble Telescope, it detects much longer wavelength radiation and its diffraction limit is significantly poorer than Hubble’s. Arecibo is still very useful, because important information is carried by radio waves that is not carried by visible light. (credit: Tatyana Temirbulatova, Flickr)

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 size 12{D} {} and a wavelength λ size 12{λ} {} exhibits diffraction spreading. The beam spreads out with an angle θ size 12{θ} {} given by the equation θ = 1 . 22 λ D size 12{θ=1 "." "22" { {λ} over {D} } } {} . Take, for example, a laser beam made of rays as parallel as possible (angles between rays as close to θ = size 12{θ=0°} {} as possible) instead spreads out at an angle θ = 1 . 22 λ / D size 12{θ=1 "." "22"λ/D} {} , where D size 12{D} {} is the diameter of the beam and λ size 12{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 (see [link] ). To avoid this, we can increase D size 12{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 size 12{D} {} much larger and θ size 12{θ} {} smaller.

The drawing shows a parabolic dish antenna mounted on a scaffolding tower and oriented to the right. The diameter of the dish is D. A horizontal line extends to the right from the top rim of the dish. Above the top line appears another line leaving the rim of the dish and angling up and to the right. The angle between this line and the horizontal line is labeled theta. Analogous lines appear at the bottom rim of the dish, except that the angled line extends down and to the right.
The beam produced by this microwave transmission antenna will spread out at a minimum angle θ = 1 . 22 λ / D size 12{θ=1 "." "22"λ/D} {} due to diffraction. It is impossible to produce a near-parallel beam, because the beam has a limited diameter.

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 size 12{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 size 12{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 size 12{x} {} . According to the Rayleigh criterion, resolution is possible when the minimum angular separation is

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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