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

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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 other options are wrong — (b) 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) 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) 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.

State PCS 2025 Q114 — Science & Technology PYQ with Answer

State PCS 2025 Q114 — Science & Technology PYQ with Answer