# Accession Number:

## AD0257781

# Title:

## DIFFRACTION BY A SEMI-INFINITE SCREEN WITH A ROUNDED END

# Descriptive Note:

# Corporate Author:

## NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES

# Personal Author(s):

# Report Date:

## 1961-03-01

# Pagination or Media Count:

## 1.0

# Abstract:

The diffraction of a cylindrical wave by a perfectly conducting semi-infinite thin screen with a cylindrical tip is analyzed. Three different methods are employed to find the field the geometrical theory of diffraction, an expansion in radial eigenfunctions and the Watson transformation of the angular eigenfunction expansion. The latter two methods yield the same result, which proves that the solution can be expanded in radial eigenfunctions even though they are not complete. The asymptotic form of the solution for large ka coincides precisely with the result given by the geometrical theory of diffraction. Here k equals 2 pilambda is the propagation constant of the field and a is the radius of the tip. This agreement proves that the geometrical theory is correct for this problem. The result determines how the field in the shadow depends upon the wavelength and the curvature of the shadow forming object. Author