   Chapter 27, Problem 69PE

Chapter
Section
Textbook Problem

Construct Your Own ProblemConsider diffraction limits for an electromagnetic wave interacting with a circular object. Construct a problem in which you calculate the limit of angular resolution with a device, using this circular object (such as a lens, mirror, or antenna) to make observations. Also calculate the limit to spatial resolution (such as the size of features observable on the Moon) for observations at a specific distance from the device. Among the things to be considered are the wavelength of electromagnetic radiation used, the size of the circular object, and the distance to the system or phenomenon being observed.

To determine

The construction of a problem in which the limit of angular resolution for a device and the limit to special resolution for observations at a specific distance is calculated.

Explanation

Formula used:

The smallest possible angle between two point sources is given by Rayleigh formula.

θ=1.22(λD)

Calculation:

Consider a circular object of diameter 1.30m and the average wavelength of visible light is 550nm.

By substituting these values in the above equation, we get

θ=1.22( 550× 10 9 m 1.30m)θ=5.16×107rad

Thus, the angle between just resolved sources is 5.16×107rad

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