Where would reddish purples lie on the spectrum of light, considering red light and purple light are on opposite ends of the visible spectrum? Obviously red and purple are opposite on the visible light spectrum. So how do we get colors that are reddish purple? Where would they lie on the spectrum of visible light?
 A: Red and violet are on opposite sides of the spectrum. Purple is not a spectral color at all, meaning there is no single wavelength of light that produces the color purple. Purple is instead a mixture of red and blue. Reddish purple is simply a mixture with more red than blue.
A: If you are seeing red and purple, it could be that your light source is emitting photons at those two frequencies. With the caveat, as pointed out by other answers, that purple is technically not a ('pure') spectral colour.
What I should also add is that what you see is not necessarily what it is, as your eyes' retinas have colour/wavelength dependent sensitivities (see plot below). So even a faint red component to the incident light onto your eye will look like a strong signal. Hence, light that has a strong violet component and a residual red component might appear to be reddish-purple because you see the mixture of the two plus the retina cell receptors' sensitivity.

A: Colours like purple arise when an (purple) objects absorbs certain frequencies from any incident light. The 'remaining' reflected light then 'looks' purple to us.
