The Rayleigh criterion provides a convenient way to describe the theoretical resolution (e.g. an ability to distinguish two bright objects ) of an optical system. The criterion states that two small bright sources of light can be resolved if the first diffraction minimum of the image of one source point just coincides with of further apart then the first maximum of another (see figure below). A converging lens, 11.9 mm in diameter, is used to form images of distant objects. Considering the diffraction by the lens, what angular separation must two distant point objects have in order to satisfy Rayleigh's criterion? Assume that the wavelength of the light from the distant objects is 437 nm. Provide your answer in millidegrees (mdeg).

The Rayleigh criterion provides a convenient way to describe the theoretical resolution (e.g. an ability to distinguish two bright objects ) of an optical system. The criterion states that two small bright sources of light can be resolved if the first diffraction minimum of the image of one source point just coincides with of further apart then the first maximum of another (see figure below). A converging lens, 11.9 mm in diameter, is used to form images of distant objects. Considering the diffraction by the lens, what angular separation must two distant point objects have in order to satisfy Rayleigh's criterion? Assume that the wavelength of the light from the distant objects is 437 nm. Provide your answer in millidegrees (mdeg).

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter36: Applications Of The Wave Model

Section: Chapter Questions

Problem 6PQ

See similar textbooks

Similar questions

Many circular apertures are adjustable, such as the pupil of your eye or the shutter of a camera. Describe the change in the diffraction pattern as such an aperture decreases in size.
The Rayleigh criterion provides a convenient way to describe the theoretical resolution (e.g. an ability to distinguish two bright objects ) of an optical system. The criterion states that two small bright sources of light can be resolved if the first diffraction minimum of the image of one source point just coincides with of further apart then the first maximum of another (see figure below). A converging lens, 22.8 mm in diameter, is used to form images of distant objects. Considering the diffraction by the lens, what angular separation must two distant point objects have in order to satisfy Rayleigh's criterion? Assume that the wavelength of the light from the distant objects is 640 nm. Provide your Page 1 answer in millidegrees (mdeg).
The Rayleigh criterion provides a convenient way to describe the theoretical resolution (e.g. an ability to distinguish two bright objects ) of an optical system. The criterion states that two small bright sources of light can be resolved if the first diffraction minimum of the image of one source point just coincides with of further apart then the first maximum of another (see figure below). A converging lens, 34.2 mm in diameter, is used to form images of distant objects. Considering the diffraction by the lens, what angular separation must two distant point objects have in order to satisfy Rayleigh's criterion? Assume that the wavelength of the light from the distant objects is 431 nm. Provide your answer in millidegrees (mdeg). Answer: Choose... +
Often in optics scientists take advantage of effects that require very high intensity light. To get the desired effect a scientist uses a laser with power P = 0.0015 W to reach an intensity of I = 350 W/cm2 by focusing it through a lens of focal length f = 0.15 m. The beam has a radius of r = 0.0011 m when it enters the lens.Randomized VariablesP = 0.0015 WI = 350 W/cm2f = 0.15 mr = 0.0011 m Part (a) Express the radius of the beam, rp, at the point where it reaches the desired intensity in terms of the given quantities. (In other words, what radius does the beam have to have after passing through the lens in order to have the desired intensity?) Part (b) Give an expression for the tangent of the angle that the edge of the beam exits the lens with with respect to the normal to the lens surface, in terms of r and f? Part (c) Express the distance, D, between the lens's focal point and the illuminated object using tan(α) and rp. Part (d) Find the distance, D, in centimeters.
Often in optics scientists take advantage of effects that require very high intensity light. To get the desired effect a scientist uses a laser with power P = 0.0065 W to reach an intensity of I = 170 W/cm2 by focusing it through a lens of focal length f = 0.11 m. The beam has a radius of r = 0.0011m when it enters the lens. Randomized VariablesP = 0.0065 WI = 170 W/cm2f = 0.11 mr = 0.0011 Part (a) Express the radius of the beam, rp, at the point where it reaches the desired intensity in terms of the given quantities. (In other words, what radius does the beam have to have after passing through the lens in order to have the desired intensity?) Part (b) Give an expression for the tangent of the angle that the edge of the beam exits the lens with with respect to the normal to the lens surface, in terms of r and f? Part (c) Express the distance, D, between the lens's focal point and the illuminated object using tan(α) and rp. Part (d) Find the distance, D, in centimeters.…
In a biprism experiment, when a convex lens was placed between the biprism and eyepiece at a distance of 30 cm from the slit, the virtual images of the slits are found to be separated by 7 mm. If the distance between the slit and biprism is 10 cm and between the biprism and eyepiece is 80 cm, find the linear magnification of the image.
A Plane convex lens is put on a glass plate such that the convex surface of the lens touches the plane surface of the plate. An oil drop is put in between. The radius of curvature of the convex surface of the lens is 200 cm and the refractive index of both the lens and the plate is 1.52. The refractive index of oil is 1.58 and the wavelength of light used is 5000 A.a. Find the radius of the 5th bright ring for normal incidence.b. Find the number of dark rings that can be observed in Newton's rings experiment if the radius of the lens is 2 cm.
Ex.3. The acceptance angle of an optical fiber in air is 22° and has a relative refractive index difference of 3%. Estimate the numerical aperture and the critical angle of the core - cladding interface for the fiber. (Ans.: 0.37, 75.9º)
Diffraction due to a circular aperture is important in astronomy. Since a telescope has a circular aperture of finite size, stars are not imaged as points, but rather as diffraction patterns. Two distinct points are said to be just resolved (i.e., have the smallest separation for which you can confidently tell that there are two points instead of just one) when the center of one point's diffraction pattern is found in the first dark ring of the other point's diffraction pattern. This is called Rayleigh's criterion for resolvability. Consider a telescope with an aperture of diameter 1.02 m. Part D What is the angular radius 0₁ of the first dark ring for a point source being imaged by this telescope? Use 550 nanometers for the wavelength, since this is near the average for visible light. Express your answer in degrees, to three significant figures. xa — ΑΣΦ Xb 0₁ 5.39 10 = 7 √x x x <४ |X| Submit Previous Answers Request Answer ? X.10n X You have already submitted this answer. Enter a new…
The Rayleigh criterion provides a convenient way to describe the theoretical resolution (e.g. an ability to distinguish objects ) of an optical system. The criterion states that two small bright sources of light can be resolved if the first d mìnimum of the image of one source point just coincides with of further apart then the first maximum of another (s Ho Your c below). A converging lens, 28.7 mm in diameter, is used to form images of distant objects. Considering the diffractio lens, what angular separation must two distant point objects have in order to satisfy Rayleigh's criterion? Assume t Here wavelength of the light from the distant objects is 469 nm. Provide your answer in millidegrees (mdeg). STE Exp complexity subscibers Answer: Choose... + Check Finishin Check c
Ex.3. The acceptance angle of an optical fiber in air is 22° and has a relative refractive index difference of 3%. Estimate the numerical aperture and the critical angle of the core – cladding interface for the fiber.
Optical fibers are constructed with a cylindrical core surrounded by a sheath of cladding material. Common materials used are pure silica (n2 = 1.450) for the cladding and silica doped with germanium (n1 = 1.465) for the core. (a) What is the critical angle θcrit for light traveling in the core and reflecting at the interface with the cladding material? (b) The numerical aperture (NA) is defined as the angle of incidence θi at the flat end of the cable for which light is incident on the core–cladding interface at angle θcrit. Show that sin θi = √(n21 - n22) . (c) What is the value of θi for n1 = 1.465 and n2 = 1.450?