Consider the following statements about a microscope and a telescope : 1. Both the eyepiece and the objective of a microscope are convex lenses. 2. The focal length of the objective of a telescope is larger than the focal length of its eyepiece. 3. The magnification of a telescope increases with the increase in focal length of its objective. 4. The magnification of a microscope increases with the increase in focal length of its objective. Which of the statements given above are correct?
- (a)1 and 3 only
- (b)1 and 4
- (c)2, 3 and 4
- (d)1, 2 and 3
Correct — D, statements 1, 2 and 3. Statement 1 is true: a compound microscope uses a convex objective to form a real, inverted, magnified image, and a convex eyepiece to view that image as a magnified virtual one, so both are converging lenses. Statement 2 is true: an astronomical telescope in normal adjustment has its objective and eyepiece separated by the sum of their focal lengths, and the objective's focal length is much the larger of the two — a long objective and a short eyepiece. Statement 3 is true and follows directly, because the angular magnification of a telescope is f₀/fₑ, so raising the objective's focal length raises the magnification. Statement 4 is the odd one out, and it is false: in a microscope the magnifying power varies inversely with the objective's focal length, so a longer-focus objective magnifies less, not more.
- (a)1 and 3 only — It drops statement 2, which is true. A telescope objective must have a long focal length precisely so that the ratio f₀/fₑ is large; the same fact that makes statement 3 true guarantees statement 2 as well.
- (b)1 and 4 — It keeps the one false statement in the set. Statement 4 applies the telescope rule to a microscope, but the two instruments scale in opposite directions — the microscope wants short focal lengths in both lenses, which is why its objective is a small, strongly curved lens.
- (c)2, 3 and 4 — It both drops the true statement 1 and retains the false statement 4. Every lens in an ordinary compound microscope is converging; there is no concave element in the basic design.
Both instruments are two-lens systems in which the objective forms an image that the eyepiece then magnifies, but they are built for opposite tasks and so scale in opposite directions. A telescope looks at distant objects that are already large but subtend a tiny angle, so its angular magnification is f₀/fₑ, and the design calls for a long-focus objective and a short-focus eyepiece. A microscope looks at a tiny object placed just outside the objective's focus, so its magnifying power is roughly (L/f₀)(D/fₑ), where L is the tube length and D the least distance of distinct vision — both focal lengths sit in denominators, so both lenses must be short-focus.
The economical way to handle this item is to settle statement 3 and statement 4 together, because they are the same sentence written for two different instruments and they cannot both be true. For a telescope the objective's focal length is on top of the magnification formula; for a microscope it is underneath. Once you see that, statement 4 falls, and only option (d) among the four excludes it while keeping statement 2. A physical check helps too: the objective of a telescope is a large lens at the far end of a long tube, while a microscope objective is a stubby lens that must be brought within millimetres of the slide.
- Both the objective and the eyepiece of a compound microscope are convex (converging) lenses.
- The angular magnification of an astronomical telescope in normal adjustment is f₀/fₑ, and its tube length is f₀ + fₑ.
- A telescope therefore uses a long-focal-length objective and a short-focal-length eyepiece.
- The magnifying power of a compound microscope varies inversely with both focal lengths, so both lenses are short-focus.
- Carrying the telescope rule across to the microscope. The objective's focal length raises magnification in one and lowers it in the other.
- Assuming a microscope must contain a concave lens because the image is inverted; the inversion comes from the real image formed by the convex objective.
- Confusing magnifying power with resolving power — a bigger image is not automatically a more detailed one.
NDA asks which lens of an instrument has the longer focal length, how magnification changes when a focal length is altered, or which of several statements about the two instruments are correct.
Which one of the following statements is correct about the magnification of an optical microscope ?
- (a) Magnification increases with the increase in focal length of eyepiece
- (b) Magnification increases with the increase in focal length of objective
- (c) Magnification does not depend upon the focal length of eyepiece
- (d) Magnification decreases with the increase in focal length of eyepiece
Answer(d) Magnification decreases with the increase in focal length of eyepiece
Its option (b) is word for word the false statement 4 of this card, marked wrong there too — the clearest confirmation that a microscope's objective works the opposite way to a telescope's.
Which one of the following telescopes contains only mirrors?
- (a) Galilean telescope
- (b) Keplerian telescope
- (c) Newtonian telescope
- (d) Schmidt telescope
Answer(c) Newtonian telescope
Extends the telescope half of this card to the design that avoids a long-focus objective lens altogether by using a mirror instead.
- practice — not a real PYQ
The angular magnification of an astronomical telescope in normal adjustment is given by
- (a)fₑ/f₀
- (b)f₀/fₑ
- (c)f₀ × fₑ
- (d)f₀ + fₑ
Answer(b) f₀/fₑ — objective focal length divided by eyepiece focal length, which is why the objective must be the longer-focus lens.
- practice — not a real PYQ
To increase the magnifying power of a compound microscope, one should use an objective of
- (a)larger focal length
- (b)smaller focal length
- (c)larger aperture only
- (d)concave type
Answer(b) smaller focal length — the objective's focal length sits in the denominator of the microscope's magnification, the reverse of the telescope case.