Q.An astronomical refractive telescope has an objective of focal length 20m and an eyepiece of focal length 2cm.

With $f_o=20\ \text{m}$, $f_e=2\ \text{cm}=0.02\ \text{m}$: tube length $L=f_o+f_e=20.02\ \text{m}$ (a true); magnification $M=f_o/f_e=1000$ (b true); the objective's real image is inverted and a simple eyepiece doesn't re-invert it, so the final image is inverted (c true); a larger aperture increases brightness but does not reduce chromatic aberrati …

Setting up

An astronomical (refracting) telescope in normal adjustment has $f_o=20\ \text{m}$ and $f_e=2\ \text{cm}=0.02\ \text{m}$.

(a) Tube length

In normal adjustment, the objective's image (formed at its own focal plane) coincides with the eyepiece's first focal point, so the separation between the lenses is

This matches statement (a) exactly. (a) is true.

(b) Magnifying power

For normal adjustment, the angular magnification is

This matches statement (b) exactly. (b) is true.

(c) Orientation of the final image

The objective forms a real, inverted image of the distant object at its focal plane. The eyepiece is used as a simple magnifier on that already-inverted image — a simple (single) lens used this way does not flip the image back the right way up, it only magnifies it further. So the final image seen through the telescope is inverted relative to the object. (c) is true.

(d) Aperture, brightness, and chromatic aberration …

Method: Computing Magnifying Power and Tube Length for an Astronomical Telescope

Use this method for any "given the two focal lengths, find the magnification/length/other property" question on an astronomical (refracting) telescope in normal adjustment.

Steps

Step 1: Identify the two focal lengths and convert to the same unit

List the objective's focal length $f_o$ and the eyepiece's focal length $f_e$, converting both to the same unit (usually metres or centimetres) before doing any arithmetic — mixing units is the most common source of error here.

Step 2: Apply the normal-adjustment magnification formula

This follows from the objective forming a real image at its own focus, which then sits exactly at the eyepiece's focus so the final image is at infinity (relaxed-eye viewing) — recognise this setup whenever a telescope problem doesn't specify a different image position. …