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Chapter 36: Q24P (page 1110)

Question:If someone looks at a bright outdoor lamp in otherwise dark surroundings, the lamp appears to be surrounded by bright and dark rings (hence halos) that are actually a circular diffraction pattern as in Fig. 36-10, with the central maximum overlapping the direct light from the lamp. The diffraction is produced by structures within the cornea or lens of the eye (hence entoptic). If the lamp is monochromatic at wavelength 550nm and the first dark ring subtends angular diameter 2.5o in the observer’s view, what is the (linear) diameter of the structure producing the diffraction?

Short Answer

Expert verified

The diameter of the structure producing the diffraction is 31.0μm.

Step by step solution

01

Given data

The wavelength of monochromatic light λ=550nm

The angular diameter 'ϕ'=1.25°

02

Definition of diffraction effect

When a wave hits a barrier or aperture, numerous events are referred to as diffraction. It is described as the interference or bending of waves through an aperture or around the corners of an obstruction into the geometric shadow of the obstruction or aperture.

03

Determining the diameter of the structure producing the diffraction

So the angle 'θ'=2.5/2=1.25°

The linear diameter 'd'

sinθ=1.22λdd=1.22×550×10-9msin1.25°d=3.07588×10-5m=31.0μm

Hence, the diameter is 31.0μm.

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Most popular questions from this chapter

(a) What is the angular separation of two stars if their images are barely resolved by the Thaw refracting telescope at the Allegheny Observatory in Pittsburgh? The lens diameter is 76 cm and its focal length is 14 m. Assume λ=550nm. (b) Find the distance between these barely resolved stars if each of them is 10 light-years distant from Earth. (c) For the image of a single star in this telescope, find the diameter of the first dark ring in the diffraction pattern, as measured on a photographic plate placed at the focal plane of the telescope lens. Assume that the structure of the image is associated entirely with diffraction at the lens aperture and not with lens “errors.”

A diffraction grating with a width of 2.0 cm contains 1000 lines/cm across that width. For an incident wavelength of 600 nm, what is the smallest wavelength difference this grating can resolve in the second order?

A diffraction grating has 8900 slits across 1.20 cm. If light with a wavelength of 500 nm is sent through it, how many orders (maxima) lie to one side of the central maximum?

Two yellow flowers are separated by 60 cm along a line perpendicular to your line of sight to the flowers. How far are you from a flower when they are at the limit of resolution according to the Rayleigh criterion? Assume the light from the flowers has a single wavelength of 550 nm and that your pupil has a diameter of 5.5 mm.

Suppose that the central diffraction envelope of a double-slit diffraction pattern contains 11 bright fringes and the first diffraction minima eliminate (are coincident with) bright fringes. How many bright fringes lie between the first and second minima of the diffraction envelope?
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