Why angular separation versus distance

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Wiki tools Wiki tools Special pages. Page tools Page tools. Userpage tools. Other projects In other languages Add links. It is often called as Coefficient of Correlation. We need to define. Exercise: If you have coordinate of object A is 0, 0 and coordinate of object B is 1, 1 , what is the angular separation? What happen if you have coordinate of object A is , while coordinate of object B is Figure 3. 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.

The answer in Part 2 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. Figure 4 shows another mirror used to observe radio waves from outer space.

Figure 4. A 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. Arecibo is still very useful, because important information is carried by radio waves that is not carried by visible light.

Diffraction is not only a problem for optical instruments but also for the electromagnetic radiation itself. 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 Figure 5. To avoid this, we can increase D. This is done for laser light sent to the Moon to measure its distance from the Earth.

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 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 Figure 6a we have two point objects separated by a distance x. According to the Rayleigh criterion, resolution is possible when the minimum angular separation is.

Figure 6. Another way to look at this is by re-examining the concept of Numerical Aperture NA discussed in Microscopes. There, NA is a measure of the maximum acceptance angle at which the fiber will take light and still contain it within the fiber. Figure 6b shows a lens and an object at point P.

The NA here is a measure of the ability of the lens to gather light and resolve fine detail. From the Figure and again using the small angle approximation, we can write. In a microscope, NA is important because it relates to the resolving power of a lens.

A lens with a large NA will be able to resolve finer details. Lenses with larger NA will also be able to collect more light and so give a brighter image. Turn in all your measurements and calculations. Tips on making measurements When you measure the building or the sculpture, always keep the cross staff level with the ground, not tilted up or down.

When you make a measurement, it should really be a series of 3 to 5 repeated measurements of the same thing. Then take the average of these as your best value, as well as stating how far above and below this average your individual data points varied. This is an estimate of the error in your measurement. Constructing the Cross-Staff To construct your cross-staff, follow the instructions below carefully. You will need good sharp and pointy!