In a drill bit which has hard-faced cutting or gauge protection elements positioned to be in direct contact with subterranean formation as the bit is rotated, at least one of these elements includes a window positioned to be in direct contact with the formation or cuttings from the formation as the bit rotates and moves forward to drill into the formation. Electromagnetic radiation with wavelength in the range from 100 nm to 2600 nm is transmitted through the window to the formation in contact with the window. Electromagnetic radiation such as fluorescence that returns through the same window is received by a spectrometer. The source and receiver of electromagnetic radiation are both accommodated within the downhole drilling equipment but spaced from the windowed element. The electromagnetic radiation travels along light guides from the source to the window and from the window to the receiver.