OK, but we sometimes have to work for knowledge - most often it doesn't just appear for the asking. Reading the various BTH posts here there is some very interesting stuff about the different BTH headlamps, and the P&H-like variants, with the different configurations of switches (bakelite knob or alloy blade) etc. There are clear variations in the detail of body shape and rims, switches, and meter positions.
I'm interested, but I'm not an expert. However I can say that by 1930 all headlamps worked by positioning the filament of the globe at the focal point of a parabolic reflector, so, yes, there is a separate reflector. But to get the details, you need to be really specific about exactly which headlamp you have, and let us know what is there and what is not.
With the internet, there is info everywhere. The Vintage Motor Cycle Club (UK) has a library with an online catalogue. They have the following:
BTH Ignition and Lighting sets, types PBK, PBM, 1930, 28 pages
https://library.vmcc.net/Catalogue/Details/79088BTH Ignition and Lighting sets, types PBK, PBM, Forms A&B, 1927, 11 pages
https://library.vmcc.net/Catalogue/Details/79089BTH Generator lighting set, type PA for Douglas, 1930-33, 12 pages
https://library.vmcc.net/Catalogue/Details/78581Maybe the answer to your query is in one of these? If you're a member of a club affiliated with the VMCC, you're welcome to use VMCC facilities, and the librarian might be able to help.
Leon