Q&A: Cassegrain Optics

Question: We’ve got a classic Cave Cassegrain scope that we’re setting up at the Mount Meru Astronomical Observatory, and we have a question about the optics. The owner’s manual says the focal length is 192″. This doesn’t make sense. The distance from the primary to the secondary is something like 42″. Multiply by two to bring the light back to the primary, then add 6″ for the drawtube, and you have at most 90″. What am I missing? — KS, MMAO, Tanzania

Answer: What you say would work if the secondary were a planar (flat) mirror. Look at that manual closely and you’ll see they’re citing an EFL (effective focal length) and not simply a “focal length”, as they would for a refractor or a basic Newtonian reflector. In Cassegrain optics the secondary is usually convex. This creates a kind of “magnifying” effect that increases the focal length to more than you could fit in the tube. Here’s another way to visualize this: If the secondary were planar (which it was in early designs), then all you’ve done is “folded” the light path, in which case you CAN add the physical distances up to the total focal length (as you were trying to do). Planar secondary optics are shown in the top graphic.

When the secondary is convex, the convergence angle of the light cone is reduced to a smaller angle. This increases the distance required for the cone to converge to a focal point. The optics behaves as though the primary is farther from the secondary than it really is. This is what increases the EFL to a value greater than the physical length of the light path. Convex secondary optics are shown in the bottom graphic.

Controlling the path of light in this manner represented a significant advance in telescope design. And it was based on one of the simplest principles of optics: When light reflects from a surface it follows the Law of Reflection …

The normal is a line drawn perpendicular to the surface at the point of reflection. On a curved mirror the direction of the normal changes continuously across the surface. This also changes the angle θ. By carefully engineering that curvature you can control the path light takes through the optical system. The actual curvature of the secondary can follow several mathematical models, depending on what optical effect is desired. The same is true for the primary, which is always concave.

Cassegrain optics were invented in the 17th century as a means for economically increasing focal length (and thus magnification) without constructing physically longer tubes. Longer tubes will flex, distorting the optics, and so require elaborate support structures as seen in this drawing of a 36 meter (120 ft) scope built by Christiaan Huygens ca. 1650.

Telescope design is all about controlling the path of light. The recent invention of adaptive optics takes that dictum to its extreme. This design uses deformable mirrors flexed by computer-driven pressure actuators. The mirror surface optically “adapts” to compensate for the effects of atmospheric distortion — what is commonly called twinkling. The shape of the mirror can change up to 1000 times each second, adjusting the curvature to significantly reduce that distortion.

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