Optical Instruments: The Telescope

A microscope lets you magnify the tiny, but what about objects that are already large yet impossibly far away? Stars, planets, and distant landmarks fill almost no angle at your unaided eye, so their details stay hidden. The telescope solves this by collecting light over a wide opening and bending it so that distant objects fill a much larger angle at your eye, making them appear closer and revealing features you could never see otherwise.

How a Refracting Telescope Works

A refracting telescope, like a compound microscope, uses two converging lenses: an objective and an eyepiece. However, the design priorities are reversed. In a microscope, both lenses have very short focal lengths. In a telescope, the objective has a large focal length and a much larger aperture (opening diameter) than the eyepiece. The eyepiece still has a short focal length, just as in a microscope.

Here is what happens step by step:

Light from a distant object arrives at the objective as nearly parallel rays (because the object is very far away).
The objective converges these rays and forms a real image at its second focal point, inside the telescope tube.
The eyepiece is positioned so that this real image sits at or near its own focal point.
The eyepiece then magnifies this intermediate image, producing a final virtual, inverted image that the observer sees.

Fig 9.25: A refracting telescope with objective and eyepiece

Deriving the Magnifying Power

The magnifying power $m$ of a telescope is defined as the ratio of the angle $\beta$ subtended at the eye by the final image to the angle $\alpha$ that the distant object subtends at the objective (or equivalently, at the unaided eye, since the object is so far away that the angle is essentially the same).

$m \approx \frac{\beta}{\alpha} \qquad \text{(definition)}$

Consider the intermediate image of height $h$ formed at the focal plane of the objective. From the geometry of the objective side, the distant object subtends an angle:

$\alpha \approx \frac{h}{f_o}$

where $f_o$ is the focal length of the objective. This follows because the image forms at distance $f_o$ from the objective and has height $h$ .

On the eyepiece side, this same image of height $h$ sits at (or very near) the focal point of the eyepiece. The angle it subtends when viewed through the eyepiece is:

$\beta \approx \frac{h}{f_e}$

where $f_e$ is the focal length of the eyepiece.

Now take the ratio:

$m \approx \frac{\beta}{\alpha} \approx \frac{h/f_e}{h/f_o} = \frac{h}{f_e} \times \frac{f_o}{h} = \frac{f_o}{f_e} \qquad \text{(9.46)}$

The image height $h$ cancels out. The magnifying power depends only on the ratio of the two focal lengths. A longer focal length objective and a shorter focal length eyepiece together give higher magnification.

Tube Length in Normal Adjustment

When the telescope is set for comfortable viewing with the final image at infinity (relaxed eye), the eyepiece is placed so that the intermediate image falls exactly at its focal point. The distance from the objective to the intermediate image is $f_o$ , and from the intermediate image to the eyepiece is $f_e$ . So the total length of the telescope tube is:

$\text{Tube length} = f_o + f_e$

This means high-magnification refracting telescopes tend to be physically long, since a large $f_o$ is needed for high $m$ .

Putting the Numbers to Work

Consider a telescope with $f_o = 100$ cm and $f_e = 1$ cm. The magnifying power is:

$m = \frac{f_o}{f_e} = \frac{100}{1} = 100$

Now imagine a pair of stars that are separated by just 1 minute of arc (1’) as seen by the unaided eye. Through this telescope, they appear separated by:

$100 \times 1' = 100' = \frac{100}{60}° \approx 1.67°$

That tiny, nearly invisible gap between two pinpoints of light becomes a clearly visible angular separation of almost two degrees.

Terrestrial Telescopes: Making the Image Upright

An astronomical telescope produces an inverted image, which is perfectly fine for looking at stars and planets (there is no “right way up” in space). For viewing objects on Earth, though, you need an upright image. A terrestrial telescope solves this by adding an extra pair of inverting lenses between the objective and the eyepiece. These lenses flip the image so the final view is erect. Refracting telescopes can serve both terrestrial and astronomical purposes.

Why the Objective Diameter Matters

For an astronomical telescope, magnification is just one part of the story. Two other properties matter enormously, and both depend on the diameter of the objective, not its focal length:

Light gathering power scales with the area of the objective. A bigger objective collects more photons per second, making it possible to observe fainter objects like distant galaxies or dim nebulae.
Resolving power is the ability to distinguish two objects that are very close together in the sky (nearly the same direction). A larger objective diameter improves resolving power, letting the telescope separate two closely spaced stars that a smaller telescope would blur into one.

The goal for astronomical telescopes, therefore, is to build objectives with the largest possible diameter.

The Limits of Refracting Telescopes

Making a very large lens runs into serious practical problems:

Weight: A large glass lens is extremely heavy. It can only be supported by its edges (you cannot put supports behind it, since light must pass through), and this makes mounting it securely very difficult.
Manufacturing difficulty: Producing a large, high-quality lens free from defects is expensive and technically demanding.
Chromatic aberration: Glass refracts different wavelengths of light by different amounts. A large lens focuses blue light and red light at slightly different points, producing colour fringes around the image. Correcting this in a single large lens is extremely hard.

The largest refracting telescope ever built has an objective diameter of about 40 inches (roughly 1.02 m), housed at the Yerkes Observatory in Wisconsin, USA. No larger refractor has ever been attempted, because these problems become unmanageable at bigger sizes.

Reflecting Telescopes: Mirrors Instead of Lenses

All of the difficulties above disappear when you replace the objective lens with a concave mirror. Telescopes built this way are called reflecting telescopes, and they dominate modern astronomy. Here is why mirrors win:

No chromatic aberration. A mirror reflects all wavelengths identically, so there is no colour fringing at all.
Much lighter. A mirror weighs far less than a glass lens of the same size and optical quality.
Better support. A mirror can be supported over its entire back surface, not just at its rim. This makes it structurally much more stable and allows truly enormous mirrors to be built.

The Problem with Reflecting Telescopes

There is one obvious challenge: a concave mirror reflects light back towards the incoming direction, so the focal point sits inside the telescope tube. The eyepiece and the observer need to be placed right there, which means they block some of the incoming light.

For very large telescopes, this blockage is a small fraction of the total light collected and is acceptable. The 200-inch (roughly 5.08 m) Mt. Palomar telescope in California takes this approach directly: the observer sits in a small cage near the focal point of the primary mirror, inside the tube.

The Cassegrain Design: A Clever Folded Path

A more elegant solution is to redirect the converging light before it reaches the focal point, using a secondary mirror. The Cassegrain telescope (named after its inventor) does exactly this:

A large concave primary mirror collects incoming parallel light and begins converging it.
Before the light reaches the focal point, a small convex secondary mirror intercepts it and reflects it back.
The reflected light passes through a hole in the centre of the primary mirror and reaches the eyepiece, which sits behind the primary.

Fig 9.26: Schematic of a Cassegrain reflecting telescope

The convex secondary mirror effectively “folds” the optical path back on itself, which achieves a large effective focal length in a physically short tube. The observer sits comfortably behind the primary mirror, out of the light path, and the small central hole blocks very little of the total mirror area.

Notable Telescopes Around the World

Telescope	Location	Type	Objective Diameter
Yerkes Observatory	Wisconsin, USA	Refracting	~1.02 m (40 in)
Mt. Palomar	California, USA	Reflecting	~5.08 m (200 in)
Kavalur Observatory	Tamil Nadu, India	Reflecting (Cassegrain)	2.34 m
Keck Telescopes (pair)	Hawaii, USA	Reflecting	10 m each

The Kavalur telescope is the largest in India. It is a 2.34 m Cassegrain reflector that was ground, polished, and installed by the Indian Institute of Astrophysics, Bangalore. The Keck telescopes in Hawaii hold the record as the largest reflecting telescopes, each with a mirror diameter of 10 metres.

Refracting vs. Reflecting Telescopes: A Quick Comparison

Feature	Refracting (Lens)	Reflecting (Mirror)
Chromatic aberration	Present; hard to eliminate in large lenses	Absent; mirrors reflect all wavelengths equally
Weight of objective	Heavy; glass must be thick for large diameters	Much lighter for equivalent optical quality
Support method	Edges only (light must pass through)	Entire back surface can be used
Maximum practical size	~1 m (Yerkes, 40 in)	10 m and beyond (Keck)
Light blockage	None (light passes straight through)	Some blockage by secondary mirror or observer cage
Use for terrestrial viewing	Yes, with inverting lenses	Less common for terrestrial use