Angle of Light Source for Absorbance Spectroscopy
Yes you could do what you propose provided that the light is properly collimated so that it all reaches the detector. It is quite common to place mirrors inside the sample housing of a spectrometer to  take the light out into the lab, through a sample (usually a weakly absorbing gas ) and then use a mirrors to get it back into the spectrometer. Multi-pass cells can also be used to do this. 

In atmospherical studies very long path lengths (100's metres) are sometimes used to identify trace amounts of various species. Of course if you do something like this you have to make sure extraneous light does not reach your detector.