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.