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Chapter 36: Q80P (page 1114)

The pupil of a person鈥檚 eye has a diameter of 5.00 mm. According to Rayleigh鈥檚 criterion, what distance apart must two small objects be if their images are just barely resolved when they are 250 mm from the eye? Assume they are illuminated with light of wavelength 500 nm

Short Answer

Expert verified

The distance between two small objects is 3.05脳10-5m

Step by step solution

01

Identification of given data

The given data can be listed below,

  • The diameter of the eye is,d=5.00mm
  • The wavelength of the light is,位=500nm
  • The distance of image from eye is,L=250mm
02

Concept/Significance of Rayleigh criterion

According to the Rayleigh criterion, there must be a minimum distance between two light sources in order for them to be resolved into separate objects.

03

Determination of the distance that two small objects must be apart

The Rayleigh angle is given by,

胃R=1.22位d=DLD=1.22位Ld

Here,位 is the wavelength of the light, dis the diameter of eye.

Substitute all the values for distance between two objects,

D=1.22500脳10-9m250脳10-3m5脳10-3m=3.05脳10-5m

Thus, the distance between two small objects is 3.05脳10-5m.

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Most popular questions from this chapter

A grating has 350 rulings/mm and is illuminated at normal incidence by white light. A spectrum is formed on a screen 30.0 cm from the grating. If a hole 10.0 mm square is cut in the screen, its inner edge being 50.0 mm from the central maximum and parallel to it, what are the (a) shortest and (b) longest wavelengths of the light that passes through the hole?

A circular obstacle produces the same diffraction pattern as a circular hole of the same diameter (except very near u 0).Airborne water drops are examples of such obstacles. When you see the Moon through suspended water drops, such as in a fog, you intercept the diffraction pattern from many drops. The composite of the central diffraction maxima of those drops forms a white region that surrounds the Moon and may obscure it. Figure 36-43 is a photograph in which the Moon is obscured. There are two faint, colored rings around the Moon (the larger one may be too faint to be seen in your copy of the photograph). The smaller ring is on the outer edge of the central maxima from the drops; the somewhat larger ring is on the outer edge of the smallest of the secondary maxima from the drops (see Fig. 36-10).The color is visible because the rings are adjacent to the diffraction minima (dark rings) in the patterns. (Colors in other parts of the pattern overlap too much to be visible.) (a) What is the color of these rings on the outer edges of the diffraction maxima? (b) The colored ring around the central maxima in Fig. 36-43 has an angular diameter that is 1.35 times the angular diameter of the Moon, which is 0.50掳. Assume that the drops all have about the same diameter. Approximately what is that diameter?

A diffraction grating has 200 lines/mm. Light consisting of a continuous range of wavelengths between 550 nm and 700 nm s incident perpendicularly on the grating.

(a) What is the lowest order that is overlapped by another order?

(b) What is the highest order for which the complete spectrum is present?

Light of wavelength 500nm diffracts through a slit of width2渭m and onto a screen that is 2maway. On the screen, what is the distance between the center of the diffraction pattern and the third diffraction minimum?

The full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern. (See Fig.36-8b.) (a) Show that the intensity drops to one-half the maximum value when sin2伪=伪22. (b) Verify that 伪=1.39rad. (about 80掳) is a solution to the transcendental equation of (a). (c) Show that the FWHM is 螖胃=2sin-10.443位/awhere a is the slit width. Calculate the FWHM of the central maximum for slit width (d) 1.00位 ,(e) 5.00位,and (f) 10.00位.
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