I've written before on this website (more than once) about the perils of asking who invented certain things, such as the telescope, the thermometer or the flushing toilet.
The first person to describe a reflecting telescope was the Scottish astronomer and mathematician James Gregory, in 1663. The first practical reflecting telescope (using a convex secondary mirror) was built in 1668 by Isaac Newton. The English polymath Robert Hooke built the first Gregorian telescope (i.e. one that used Gregory's design), in 1673.
In 1672, a French scientific journal described a reflecting telescope that largely superseded the Gregorian reflector as the alternative to the Newtonian design. This is known as the Cassegrain design, but the actual identity of its inventor has always been shrouded in mystery. Current thinking seems to favour a French priest named Laurent Cassegrain.
What is invention? Is it having the idea, or is it putting the idea into practice with a working model?
If the former, then I would suggest that the inventor of the reflecting telescope was James Gregory. If the latter, I would agree with the question setter; it was Isaac Newton.
James Gregory, admittedly, didn't live from 1642 to 1726. (He was born in 1638, and died in 1675 – at the age of only 36 – of a stroke, while observing the moons of Jupiter with his students.) But the ambiguity could have been avoided altogether by asking something like "Which English scientist, who lived from 1642 to 1726, built the first practical reflecting telescope, in 1668?"
Reflecting telescopes are cheaper to make than refractors, but the design has to overcome the problem of allowing the viewing of an image without obstructing the primary mirror. The Gregorian, Newtonian and Cassegrain designs all use different methods to do this.
Cassegrain reflectors can be more compact than Newtonians, because the light is 'folded' twice inside the tube, making two journeys rather than one. But the Newtonian is cheaper to make.
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