The input impedance of a short-circuited lossless transmission line guarter wave long is

A uniform plane electromagnetic wave traveling in free-space enters into a lossless medium at normal incidence. In the medium its velocity reduces by 50% and in free space sets up a standing wave having a reflection coefficient of - 0.125. Calculate the permeability and the permittivity of the medium.

In a board side array of 20 isotropic radiators, equally spaced at a distance of $$\lambda /2$$, the veam width between first nulls is

In the radiation pattern of a 3-element array of isotropic radiators equally spaced at distances of $${\lambda /4}$$ it is required to place a null at an angle of 33.56 degrees off the end-fire direction. Calculate the progressive phase shifts to be applied to the elements. Also calculate the angle at which the main beam is placed for this phase distribution.