In a simple astronomical telescope, the objective and the eyepiece used respectively, are :

Correct — D, a convergent lens and a convergent lens. A simple astronomical telescope is the Keplerian refractor, and both of its lenses converge. The objective faces the sky and has a long focal length and a wide aperture; light arriving from a distant star is effectively parallel, and a converging lens brings it to a real image just inside the tube, at the objective's second focal point. A diverging lens could not do this — it spreads parallel light apart and forms only a virtual image, which there would be no way to examine. The eyepiece is then used exactly as a magnifying glass, placed so that this small real image sits at or just inside its own focus, and a magnifying glass is a converging lens. The tube is therefore about fo + fe long and the magnifying power is fo/fe, which is why observatory refractors are long instruments with a short eyepiece. The final image comes out inverted, and for astronomy that does not matter — a star field looks the same either way up. If the wrong-way-up image does matter, as when looking at things on the ground, a terrestrial telescope adds a further pair of lenses purely to turn the image the right way round.

• (a)a convergent lens and a divergent lens. — A real instrument, but not this one. This is the Galilean telescope, with a plano-convex objective and a plano-concave eyepiece, and its advantage is an erect image in a short tube. Its field of view is narrow, which is why the Keplerian design replaced it for astronomy.
• (b)a divergent lens and a divergent lens. — A diverging objective cannot bring starlight to a real image inside the tube, so there is nothing for the eyepiece to magnify. No telescope is built this way.
• (c)a divergent lens and a convergent lens. — The Galilean arrangement with the two lenses swapped. The objective is the lens that must gather and converge light from the sky, and a diverging lens does the opposite.

A refracting telescope has two jobs. The objective gathers light and forms a real image of a distant object; the eyepiece magnifies that image for the eye. Magnifying power is the ratio fo/fe, so a long objective focal length and a short eyepiece focal length give high magnification. But the quantity that really matters in astronomy is the diameter of the objective, because both the light-gathering power and the resolving power depend on it. That is why large telescopes are described by their aperture rather than their magnification.

The route to the answer is to ask what each lens has to do rather than to recall a picture. Forming a real image of a distant object is something only a converging lens can do, so the objective is settled at once and options (b) and (c) fall away. Then ask what an eyepiece is: it is a magnifying glass held to the eye, and a magnifying glass converges. That leaves (d) and rules out (a). Keep Galileo's design in mind as the named exception rather than as a competitor — a converging objective with a diverging eyepiece, short and giving an upright view, which is essentially the arrangement still used in opera glasses. Note also why big telescopes stopped using lenses at all. NCERT records that the largest lens objective in use is the 40-inch at Yerkes Observatory in Wisconsin; a lens that size sags under its own weight and can only be supported at its rim, and it disperses colours. A mirror has no chromatic aberration and can be supported over its whole back, so modern instruments use a concave mirror as the objective. The largest telescope in India, the 2.34-metre instrument at Kavalur in Tamil Nadu, is a reflector of the Cassegrain type.

• In a simple astronomical telescope both lenses converge: a long-focal-length objective and a short-focal-length eyepiece.
• The objective forms a real image of the distant object at its second focal point; the eyepiece magnifies that image.
• Magnifying power is fo/fe and the tube length is about fo + fe; the final image is inverted.
• The Galilean telescope uses a converging objective with a diverging eyepiece and gives an erect image in a shorter tube.
• The largest lens objective in use is the 40-inch refractor at Yerkes Observatory; the largest telescope in India, at Kavalur, is a 2.34-metre Cassegrain reflector.

• Picking the Galilean arrangement; it is a genuine telescope but not the simple astronomical one.
• Assuming an inverted image means something is wrong with the instrument — the Keplerian design always inverts, and astronomers do not care.
• Confusing magnification with power. Aperture, not magnification, is what decides how faint an object a telescope can show.

As a lens-type question like this, as a magnifying-power or tube-length numerical using fo/fe and fo + fe, or as a statements item comparing the microscope with the telescope.

• practice — not a real PYQ

  In an astronomical telescope of magnifying power 20, the eyepiece has a focal length of 5 cm. The focal length of the objective is:

  • (a)4 cm
  • (b)25 cm
  • (c)100 cm
  • (d)0.25 cm

  Answer(c) 100 cm — magnifying power is fo/fe, so fo = 20 × 5 = 100 cm, and the tube is about 105 cm long.

• practice — not a real PYQ

  Which one of the following telescopes produces an erect final image without any additional lenses?

  • (a)The Keplerian astronomical telescope
  • (b)The Galilean telescope
  • (c)The Newtonian reflector
  • (d)The Cassegrain reflector

  Answer(b) The Galilean telescope — its diverging eyepiece gives an upright image in a short tube, which is why the arrangement survives in opera glasses.