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27.6 Limits of Resolution: The Rayleigh Criterion
The slit is a few times larger than the wavelength of light.
This is consistent with the fact that light must interact with an object similar in size to its wavelength in order to exhibit significant wave effects.
The central maximum is extended on either side of the original beam.
The angle between the first and second minima is very small.
The second maximum is half as wide as the central one.
Light diffracts as it moves through space, bending around obstacles.
Diffraction limits the detail we can obtain in images and can be used as a spectroscopic tool.
A fuzzy edge surrounded by circles of light is obtained instead of a bright spot with sharp edges.
The pattern is caused by a single slit.
Light from different parts of the circular aperture is destructive.
The effect is most noticeable when the opening is small, but it's also noticeable when the opening is large.
It is not possible to tell if there are two light sources or one light source.
The wave nature of light causes this limit to be inescapable.
Diffraction limits the resolution in many situations.
Our vision is limited by the light that passes through our eye.
The spread of light is due to the limited diameter of a light beam, not to the interaction with an aperture.
Light passing through a lens with a diameter shows this effect and spreads, just as light passing through an ape of diameter does.
Diffraction limits the resolution of any system with a lens or mirror.
It can be shown that the first minimum in the pattern occurs when the diameter of the instrument is larger than the wavelength of light.
Lord Rayleigh developed the accepted criterion for determining the diffraction limit to resolution based on this angle in the 19th century.
The expression has units of radians.
The central maximum is larger and brighter than the sides.
The criterion for being resolvable is shown here.
The maximum of one pattern is on the first minimum of the other.
The size and shape of objects are limited by the wavelength of the probe.
When extremely small wavelength probes are used, the system is disturbed, still limiting our knowledge, much as making an electrical measurement alters a circuit.
In quantum mechanics, Heisenberg's uncertainty principle asserts that the limit is inescapable.
The Hubble Space Telescope's primary mirror has a diameter of 2.40 m. The light wavelength is assumed to be between 550 and 600 nm.
The smallest angle between point sources is given by the criterion stated in the equation.
Since we are given how far away the stars are, the distance can be calculated.
The two objects are separated by an angle.
The angle found in part (a) is very small, because the primary mirror is so large compared to the wavelength of light.
Diffraction effects are most noticeable when light interacts with objects having sizes on the order of the wavelength of light.
The effect is still there and there is a limit to what can be seen.
The resolution of the Hubble Telescope is not as good as found here.
There are other effects, such as non-uniformities in mirrors, that limit resolution.
It gives an indication of the size and quality of the Hubble because it is above the Earth's atmosphere.
The Hubble Space Telescope and a ground-based telescope can give an idea of the observable detail.
Two stars separated by half a light year can be resolved, according to the answer.
The average distance between stars is between 5 and 1 light years in the outer parts and between 1 and 2 light years in the center.
The Hubble can resolve most of the individual stars even though it takes 2 million years for its light to reach us.
A natural bowl in Puerto Rico made into a radio telescope is lined with reflective material.
It is the largest dish in the world.
Although Arecibo is larger than the Hubble Telescope, it does not detect as much wavelength radiation as Hubble does.
Important information is carried by radio waves that are not visible.
Diffraction is a problem not only for optical instruments, but also for the radiation itself.
A beam of light has a finite diameter and a wavelength.
The beam is spread out by the equation.
A laser beam made of rays as parallel as possible spreads out at an angle, where is the diameter of the beam and is its wavelength.
The beam of the flashlight is not very parallel to start with.
This is done to measure the distance from the Earth to the Moon.
Through a telescope, the laser beam is expanded to make larger and smaller objects.
The beam produced by this antenna will spread out at a minimum angle.
The beam has a limited diameter so it is impossible to produce a near-parallel beam.
Resolution is presented when the microscope is used.
Resolution is the ability of a lens to produce sharp images of two objects.
The bigger the distance by which two objects can be separated, the better the resolution.
The distance is defined as the resolving power of a lens.
The expression for resolving power is obtained from the criterion.
Re-examining the concept of Numerical Aperture is one way to look at this.
There is a measure of the maximum acceptance angle at which the fiber will take light.
The angle at its focus is defined as.
The index of refraction of the medium between the objective lens and the object at point P is the for a lens.
It relates to the resolving power of a lens in a microscope.
A large lens will be able to resolve details.
The larger the lens, the brighter the image.
The larger the cone of light that can be brought into the lens, the more modes will be collected.
The resolving power of the microscope will be higher because it has more information to form a clear image.
The focal point of a beam has a finite width and intensity distribution.
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