The hydrogen spectrum is one of the most commonly demonstrated and most commonly studied. After the visible spectral lines (Balmer series) are explained by the Rydberg's formula, it becomes immediately apparent that there will also be similar infrared and ultraviolet series. As you may have taught your students, these are called the Paschen and the Lyman series, respectively. But do they really exist? In this article I explain how these wavelengths were first detected and go further to provide advice on modern means to more simply detect and measure invisible spectral lines. The history of these spectral lines is also presented, which gives a good flavor for the different roles of theoretical physics and applied physics in investigating a given phenomenon.