A company called Luxeon makes LED modules that I like. Consider using the white 3 Watt module. Along with mounting it to your scope somehow, you will need to mount it to a heat sink, and provide some kind of current regulated power supply for it.
The last site has the Luxeon in good range of choices, particularly interesting is the 1 watt star with optics to yield a 10 degree viewing angle beam (for 8.98). A 3 watt white star goes for $8.10. A 5 watt star costs $27.00. I like the stars because they make mounting easy (since I am not designing my own custom circuit board). I just put an order in for several of the 1 watt with optics modules. The Luxeon III in white claims a 5500K color temperature (much more like daylight that a yellow tungsten bulb that so many people seem to prefer). 100,000 hour operating life. It produces 60 lumens at 700 mA current, and 80 lumens at 1000 mA current. It has a forward voltage of 3.7 volts nominal (can be 3.03 to 4.47 volts The white version is rated for a maximum current of 1000 mA.The spectrum of the white Luxeon version has a big peak at about 440 nm (blue), almost no output at 480 nm (blue-cyan), then a broad output that peaks around 550 nm (green), and slowly tails off toward 750 nm (red). This blue peak and minimal red output accounts for the "blue cast" most people find objectionable.
Cree also has a nice LED module (for $12.90). Looking at the spec sheet, it looks a lot like the 3 Watt Luxeon. It even has the same kind of spectral curve.
NiMh batteries (the rechargeables that I like to use) yield 1.2 volts per cell, so it would take 4 of them producing 4.8 volts to drive some kind of circuit for a LED of this sort.
Tom's Mineralogy Info / tom@mmto.org