BPSC 70th CCE Re-exam Prelims Q114: As the diameter of objective lens of a telescope increases,

Q: What is the answer to BPSC 70th CCE Re-exam Prelims Q114?

A. Correct — A, Increases. A telescope cannot form a perfect point image of a star, because the light passing through its circular aperture is diffracted and spreads into a small disc surrounded by faint rings. Two stars can be told apart only when their diffraction patterns are far enough apart, and the Rayleigh criterion puts that limit at an angular separation of 1.22 times the wavelength divided by the aperture diameter — theta equals 1.22 lambda over D. Every term in that expression matters. The aperture D sits in the denominator, so making the objective bigger makes theta smaller: the smallest separation the instrument can split shrinks, which is precisely what is meant by higher resolution. Resolving power is usually written the other way up, as D divided by 1.22 lambda, so that it rises in step with the aperture. Put numbers to it and the effect is concrete: at a wavelength of 550 nanometres, a 100 mm objective has a diffraction limit of about 1.4 seconds of arc, while the 2.4 m mirror of the Hubble Space Telescope reaches about 0.05 seconds of arc. Aperture buys a second thing as well, which is why observatories chase it: the light collected goes as the area, and therefore as the square of the diameter, so doubling D collects four times the light and reaches fainter objects. Magnification, by contrast, is a matter of focal lengths and adds nothing to what the instrument can actually separate.

BPSC 70th CCE Re-exam Prelims General Studies · Question 114 of 142

Verified against the official question booklet. Answer derived — no official key exists for this edition.

Answers derived, not from the official key. BPSC published an answer key for BPSC 70th CCE Re-exam at the time, but it is no longer available from the Commission or in any web archive. The answers here are our best-supported answers — solved from the question itself and cross-checked against primary sources — and each card says how certain it is. The question text is verbatim from the official booklet. These are not the Commission's answer key.

Question order, option order and answers follow the official BPSC Booklet Series I, paper code 01/BPP/GO/CC/PT-2025(Y).

As the diameter of objective lens of a telescope increases, the resolution of telescope

(a)Increases
(b)Decreases
(c)Depends on focal length of lens
(d)Remains same

Answer

Why

Correct — A, Increases. A telescope cannot form a perfect point image of a star, because the light passing through its circular aperture is diffracted and spreads into a small disc surrounded by faint rings. Two stars can be told apart only when their diffraction patterns are far enough apart, and the Rayleigh criterion puts that limit at an angular separation of 1.22 times the wavelength divided by the aperture diameter — theta equals 1.22 lambda over D. Every term in that expression matters. The aperture D sits in the denominator, so making the objective bigger makes theta smaller: the smallest separation the instrument can split shrinks, which is precisely what is meant by higher resolution. Resolving power is usually written the other way up, as D divided by 1.22 lambda, so that it rises in step with the aperture. Put numbers to it and the effect is concrete: at a wavelength of 550 nanometres, a 100 mm objective has a diffraction limit of about 1.4 seconds of arc, while the 2.4 m mirror of the Hubble Space Telescope reaches about 0.05 seconds of arc. Aperture buys a second thing as well, which is why observatories chase it: the light collected goes as the area, and therefore as the square of the diameter, so doubling D collects four times the light and reaches fainter objects. Magnification, by contrast, is a matter of focal lengths and adds nothing to what the instrument can actually separate.

Why the others are wrong

(b)Decreases — The exact inversion of the Rayleigh criterion. It can be reached by confusing the two ways the result is stated — the limiting ANGLE decreases as the aperture grows, and someone who has memorised 'theta gets smaller' without noticing that a smaller theta means better resolution will read the trend backwards.
(c)Depends on focal length of lens — The most instructive wrong answer, because focal length does govern something — magnification, which is the ratio of the objective's focal length to the eyepiece's. But magnifying a blurred image only produces a bigger blur. Empty magnification is the standard term for pushing a telescope past what its aperture can resolve, and it is why a big number on a toy telescope's box means nothing.
(d)Remains same — This would mean the aperture does not appear in the resolution formula at all, which contradicts both the theory and every observatory built in the last two centuries. If aperture made no difference, there would be no reason to construct mirrors eight or ten metres across at enormous cost.

Concept

Three different performance figures of an optical instrument are constantly confused, and a question like this is really testing whether you keep them apart. Magnifying power is how much larger the image looks and depends on focal lengths — for a telescope, the objective's focal length divided by the eyepiece's. Light-gathering power is how faint an object can be detected and goes as the square of the aperture diameter, since it is the collecting area that matters. Resolving power is how close two objects can be and still be seen as two, and it is set by diffraction at the aperture: the Rayleigh criterion gives a minimum angle of 1.22 lambda over D for a circular opening. Only the third of these answers the question asked here. The same expression explains why radio astronomy needs enormous instruments — at metre wavelengths lambda is a million times larger than for visible light, so D must grow correspondingly, which is why the Giant Metrewave Radio Telescope near Pune spreads thirty 45-metre dishes over many kilometres and combines them so that the array behaves like one very large aperture.

Read the noun in the stem, then locate it in a formula. 'Resolution' points to theta equals 1.22 lambda over D, and once that is on the page the answer follows mechanically: D is in the denominator of the angle, so a larger D means a smaller minimum resolvable angle, which means higher resolution. The discriminating check against option (c) is to ask what focal length actually appears in — it appears in the magnification formula and nowhere in the diffraction limit, so it cannot be the controlling variable here. One honest qualification belongs on this card, because it is the difference between the theory and observatory practice: for a ground-based telescope, turbulence in the atmosphere blurs images to roughly one second of arc regardless of aperture, so beyond a certain size the extra diameter buys light-gathering power rather than sharpness until adaptive optics or a location above the atmosphere removes the limit. That is why the Hubble's modest 2.4-metre mirror outperformed far larger ground instruments in sharpness for years.

Key facts

Rayleigh criterion for a circular aperture: the minimum resolvable angular separation is theta = 1.22 λ / D, so resolving power = D / (1.22 λ) rises with aperture diameter
At λ = 550 nm a 100 mm objective is diffraction-limited to about 1.4 arcseconds; the 2.4 m mirror of the Hubble Space Telescope reaches about 0.05 arcseconds
Light-gathering power goes as the square of the aperture diameter, because it is the collecting area that counts — doubling D collects four times the light
Magnifying power of a telescope is the objective's focal length divided by the eyepiece's, and it has no bearing on the diffraction limit; pushing beyond that limit is called empty magnification
Because resolution depends on λ / D, radio telescopes must be very large or must be combined as arrays: the Giant Metrewave Radio Telescope near Narayangaon, Pune, uses thirty fully steerable 45-metre dishes observing at metre wavelengths
Atmospheric turbulence limits ground-based optical telescopes to roughly one arcsecond unless adaptive optics is used, which is why space telescopes achieve their theoretical resolution more easily

D sits in the denominator of the diffraction limit — that single placement answers the question

θ = 1.22 λ / D→The Rayleigh criterion for a circular aperture: θ is the SMALLEST angular separation at which two stars still read as two, because each is spread by diffraction into a disc with faint rings.

D grows ⇒ θ shrinks→A smaller minimum resolvable angle means the instrument splits finer detail. That is exactly what 'higher resolution' means — so resolution INCREASES.

Resolving power = D / (1.22 λ)→The same relation written the other way up, so the number rises with aperture. At λ = 550 nm: a 100 mm objective is limited to about 1.4 arcseconds; Hubble's 2.4 m mirror reaches about 0.05 arcseconds.

Where focal length actually lives→Magnifying power = f(objective) / f(eyepiece). Focal length appears nowhere in the diffraction limit, so it cannot control resolution. Magnifying past the limit is 'empty magnification' — a bigger blur.

What aperture also buys→Light-gathering power goes as the collecting AREA, i.e. as D². Doubling the diameter collects four times the light and reaches fainter objects — a separate benefit from resolution.

Two honest riders. Ground-based sharpness is capped near one arcsecond by atmospheric turbulence, so past a point extra diameter buys light rather than detail until adaptive optics or orbit removes the limit. And because resolution depends on λ/D, metre-wavelength radio work needs vast effective apertures — the GMRT combines thirty 45-metre dishes to behave as one.

Study next

Resolving power of telescopes and microscopes, and the Rayleigh criterion for circular aperturesDiffraction — single-slit patterns, the limits of ray optics, and why diffraction sets the ultimate limit on imagingOptical instruments — compound microscope and astronomical telescope, magnifying power, and reflecting versus refracting designsRadio astronomy and interferometry — the GMRT, very long baseline interferometry and the Event Horizon TelescopeMajor telescopes and observatories, including the Hubble and James Webb space telescopes and India's Devasthal and Kavalur facilities

Common traps

Reading 'the minimum resolvable angle decreases' as 'resolution decreases' — the two statements say opposite things about performance
Thinking magnification improves resolution; beyond the diffraction limit extra magnification is empty and only enlarges the blur
Forgetting that a ground telescope's practical sharpness is capped by atmospheric seeing, so the diffraction limit is a ceiling rather than a promise

BPSC asks the trend in one line — does the quantity go up, down or stay the same — so the mark is won by attaching each performance figure to its formula rather than by calculation. UPSC's General Studies paper prefers applied optics: why a shadow forms, why an endoscope works, why a CD shows rainbow colours, so the same chapter has to be revised for phenomena as well as for formulae.

Related PYQs

No directly related past PYQ was found.

Practice

practice — not a real PYQ
The magnifying power of an astronomical telescope is given by
- (a)the diameter of the objective divided by the wavelength of light
- (b)the focal length of the objective divided by the focal length of the eyepiece
- (c)the focal length of the eyepiece divided by the focal length of the objective
- (d)the square of the diameter of the objective
Answer(b) the focal length of the objective divided by the focal length of the eyepiece — a ratio of focal lengths, which is why magnification says nothing about the instrument's resolving power.
practice — not a real PYQ
If the aperture of a telescope is doubled, its light-gathering power becomes
- (a)half
- (b)double
- (c)four times
- (d)unchanged
Answer(c) four times — light-gathering power depends on the collecting area, which is proportional to the square of the diameter.