Recently I shared some self portraits shot using my Westcott X-Drop background setup and a flash shooting into my DIY "Flash Flat," as I have dubbed my homemade V-Flat made with two project presentation boards (http://www.infotor.com/blog/diy-flash-flat-and-a-self-portrait/). Well, tonight I decided to try to attach a piece of white felt material I had handy to the X-Drop frame using two tarp clamps I purchased at Home Depot for a totally different purpose. 
That worked, but I needed more clamps. Since the material piece I had was a foot too short, I was going to need something longer to secure the bottom of the fleet material to the bottom hooks. Quite by accident, I discovered some longer clips I had in my tool shed and they worked perfectly!
OK I was ready to get things set up. I first tried the "Flash Flat" I had used before, but it just didn't splash back enough light to lighten the felt background. So, I put my elective umbrella into service and placed it beside my camera on a tripod. Remember, I am using an Olympus OM-D E-M1 which has built-in Wi-Fi so that I can control the camera from my iPhone! 
This is very handy for doing these type of self portrait shoots! That worked fairly well, but it still was not lighting up the background enough. I, then cheated, and enlisted the services of a second flash to splash light on the white felt background, thus blowing it out to a pure white background behind my head.
However, since I am trying to show how one can do this with ONLY one light, I turned that flash off and moved the stand with the flash and reflective umbrella closer to me and, thus, the background. This helped, but because of the Inverse Square Law, the background still went a bit darker than I wanted and I also decided that felt is not a good material for a background! I will try this again with a different white material and see if we get better results.
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If you need help learning how to use a flash effectively, please watch for classes I schedule periodically throughout the year or get in touch to arrange some 1:1 tutoring that we can customize to your needs. Check out my Holiday Specials brochure at http://www.infotor.com/photoclasses/handouts/HolidayPromo_2014.pdf.