The Telescope

The Refracting Telescope

A telescope gives angular magnification of distant objects. Like the microscope it has an objective and an eyepiece — but with opposite design rules: the objective has a LARGE focal length and a much larger aperture than the eyepiece.

Light from the distant object forms a real image at the objective's second focus, inside the tube; the eyepiece magnifies it like a simple microscope. The magnifying power is the ratio of the angle the final image subtends at the eye ($\beta$) to the angle the object itself subtends ($\alpha$):

$$\boxed{m = \frac{\beta}{\alpha} = \frac{f_o}{f_e}}\qquad\text{with tube length } L = f_o + f_e$$

NCERT's example: $f_o = 100$ cm, $f_e = 1$ cm gives $m = 100$ (tube about 101 cm). The final image is inverted — irrelevant for stars, awkward on land: terrestrial telescopes add a pair of inverting lenses to erect the view.

Why the Big Ones Are Mirrors (Reflecting Telescopes)

For astronomy, two performance currencies matter: light-gathering power (proportional to the objective's area — faint galaxies need big collectors) and resolution (better with larger aperture). Scaling a LENS up runs into trouble; a mirror objective wins on every count (NCERT's list):

1. No chromatic aberration — reflection treats all colours identically; a big lens smears colours.
2. Spherical aberration removable — use a parabolic mirror.
3. Mechanical support is far easier: a mirror weighs less than a lens of equivalent quality and can be supported over its entire back (a lens can only be held at the rim, and a huge lens sags under its own weight).

The Cassegrain arrangement: a large concave (parabolic) primary with a hole at its centre; a small convex secondary mirror reflects the converging beam back through the hole to the eyepiece/detector. Compact tube, big effective focal length.

[NEET Important] 'Give two reasons why reflecting telescopes are preferred' — chromatic-aberration freedom and full-back mechanical support are the expected pair; the parabolic cure of spherical aberration earns the third mark.

Solved Examples

Example 1: NCERT's 100x telescope [NEET Numerical]

A telescope has $f_o = 100$ cm and $f_e = 1$ cm. Find its magnifying power and tube length.

Solution:

1. $m = \frac{f_o}{f_e} = \frac{100}{1} = 100$.
2. Tube length $= f_o + f_e = 101$ cm.
3. Long objective, short eyepiece — the exact opposite of a microscope's recipe.

Example 2: Design from constraints [JEE Numerical]

You must build a 50x telescope in a 102 cm tube (normal adjustment). Find the focal lengths.

Solution:

1. $\frac{f_o}{f_e} = 50$ and $f_o + f_e = 102$ cm.
2. $50f_e + f_e = 102 \Rightarrow f_e = 2$ cm; $f_o = 100$ cm.
3. Two equations, two unknowns — the standard telescope design problem.

Example 3: The moon through it [JEE Numerical]

The moon subtends about 0.5 degrees to the naked eye. Through the 100x telescope, what angle does its image subtend?

Solution:

1. $m = \beta/\alpha$: $\beta = m\alpha = 100 \times 0.5 = 50$ degrees.
2. The moon fills most of your visual field — angular magnification in action.
3. Telescopes do not make distant things 'bigger'; they make them subtend more angle.

Example 4: Objective image size [JEE Numerical]

For the same telescope, how large is the moon's REAL image at the objective's focus? (Moon's angle 0.5 degrees = 8.7 mrad.)

Solution:

1. Image height at the focus $= f_o\alpha$ (small angles).
2. $h = 100\text{ cm} \times 8.7\times10^{-3} = 0.87$ cm.
3. A centimetre-scale moon inside the tube, which the eyepiece then magnifies angularly.

Example 5: Why a LARGE objective aperture? [NEET pattern]

Give the two NCERT reasons telescope objectives are made as large as possible.

Solution:

1. Light gathering: collected light grows with aperture area — faint stars become visible.
2. Resolution: larger apertures separate closer star pairs (sharper detail).
3. Magnification is the cheap part; aperture is the expensive, precious one.

Example 6: Mirror vs lens objective

List NCERT's reasons the world's largest telescopes are reflectors.

Solution:

1. No chromatic aberration in a mirror (all colours reflect alike).
2. Spherical aberration eliminated by a parabolic figure.
3. Support: a mirror is lighter and can be held across its entire back; a giant lens must hang by its edges and deforms. Hence Cassegrain reflectors rule the mountaintops.

Example 7: The Cassegrain trick

Describe the Cassegrain telescope's geometry and its advantage.

Solution:

1. A large concave parabolic primary with a central hole; a small convex secondary faces it.
2. The primary's converging beam reflects off the secondary back through the hole to the focus behind the primary.
3. Folding the path makes the tube short while keeping a long effective focal length — big telescope, compact body.

Example 8: Terrestrial vs astronomical

Why do terrestrial telescopes carry extra lenses?

Solution:

1. The two-lens astronomical telescope yields an inverted final image — harmless for stars.
2. Watching ships or birds upside-down is absurd, so a pair of inverting (erecting) lenses is added in the tube.
3. Same optics otherwise; the erecting stage just flips the image upright.

Example 9: Swap test [NEET Numerical]

What happens if you look through the 100 cm/1 cm telescope the wrong way round?

Solution:

1. The roles swap: $m = \frac{f_e}{f_o} = \frac{1}{100}$.
2. Objects shrink to a hundredth of their angular size — the world recedes.
3. (Doorpeep viewers exploit exactly this minifying geometry.)

Example 10: Comparing the two instruments

Contrast microscope and telescope in one table-worth of facts.

Solution:

1. Object: microscope — tiny and near (just outside $f_o$); telescope — huge and far (at infinity).
2. Objective: microscope — small $f_o$, small aperture; telescope — large $f_o$, large aperture.
3. Magnification: $\frac{L}{f_o}\frac{D}{f_e}$ vs $\frac{f_o}{f_e}$; both invert, both use a magnifier eyepiece, both prefer the image at infinity. One pair of formulas, two opposite philosophies.