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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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