Final answer:
The 15-inch telescope at Ole Miss falls under the category of smaller, more traditional telescopes compared to the large modern observatories like Keck and the upcoming European ELT.
Step-by-step explanation:
The telescope category based on the diameter of its primary mirror at Ole Miss, measuring 15 inches, suggests it belongs to smaller, more traditional telescopes. Reflecting telescopes, pioneered since Newton's time, have scaled up significantly, with mirror sizes transitioning from inches to several meters in professional observatories. The Hale Telescope at Palomar Observatory created a milestone with a 200-inch (5-meter) mirror.
Today's notable giants like the Keck Observatory house telescopes with primary mirrors of 8 to 10 meters in diameter, composed of multiple hexagonal segments. The ambitious European Extremely Large Telescope (E-ELT) is set to dwarf these with a 39.3-meter primary mirror. Given this context, the 15-inch telescope would not fall into the category of the large, segment-based telescopes that constitute the forefront of modern astronomical research.