The light of wavelength 600 nm is coming from a star. What is the limit of resolution of a telescope whose objective has a diameter of 2.54 m?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 2.9\times10^{-7}\,\mathrm{rad} \)
The limit of resolution of a telescope, the smallest angular separation it can resolve, is given by the Rayleigh criterion \( \Delta\theta = \frac{1.22\,\lambda}{D} \), where D is the diameter of the objective.
\( \displaystyle \Delta\theta = \frac{1.22\times600\times10^{-9}\,\mathrm{m}}{2.54\,\mathrm{m}} \)
\( \displaystyle \Delta\theta = \frac{7.32\times10^{-7}}{2.54}\,\mathrm{rad} \approx 2.9\times10^{-7}\,\mathrm{rad} \)
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
Resolving Power of Optical Instruments – “… Example 10.6 Assume that light of wavelength 6000Å is coming from a star. What is the limit of resolution of a telescope whose objective has a diameter of 100 inch? Solution A 100 inch telescope implies that 2a = 100 inch = 254 cm. Thus if, λ ≅ 6000Å = 6×10–5 cm then
\( \displaystyle \Delta\theta \approx \frac{0.61 \times 6 \times 10^{-5}}{127} \approx 2.9 \times 10^{-7} \text{ radians} \)”