I agree that the attempted solution should be incorrect because of what you described, but it got the "magic number" (which could have been deduced more properly by theorizing that one axis stays the same length as the diameter of the beam of light). This brings me back to the same question ...
Homework Statement
I've pretty much given up on this problem:
"A spotlight throws a beam of light that is 25 cm in diameter. If the beam hits the stage floor at an angle of 60 degrees with the horizontal, find an equation for the elliptical pool of light on the stage floor. (Figure 2-23)"...