A telescope has an objective lens of 0.1 m diameter and is situated at a distance of 500 m from two objects. What will be the minimum distance between these two objects which can be resolved by the telescope. The mean wavelength of light is 600 nm.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3.66 mm
Because of diffraction at the objective, a telescope can separate two point objects only if the angle between them at the telescope is at least its limit of resolution, given by the Rayleigh criterion for a lens of diameter \( D \):
\( \displaystyle \Delta\theta = \frac{1.22\,\lambda}{D} \)
\( \lambda = 600\,\mathrm{nm} = 6\times10^{-7}\,\mathrm{m} \)
\( D = 0.1\,\mathrm{m} \)
\( \displaystyle \Delta\theta = \frac{1.22 \times 6\times10^{-7}}{0.1} = 7.32\times10^{-6}\,\mathrm{rad} \)
The objects are at a distance \( d = 500\,\mathrm{m} \). For a small angle, their separation is the distance multiplied by the angle (in radians):
\( x = d\,\Delta\theta = 500 \times 7.32\times10^{-6}\,\mathrm{m} \)
\( x = 3.66\times10^{-3}\,\mathrm{m} = 3.66\,\mathrm{mm} \)
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 – “… Although the size of the spot is very small, it plays an important role in determining the limit of resolution of optical instruments like a telescope or a microscope. For the two stars to be just resolved
\( \displaystyle f\,\Delta\theta \approx r_0 \approx \frac{0.61\,\lambda f}{a} \)
implying
\( \displaystyle \Delta\theta \approx \frac{0.61\,\lambda}{a} \qquad (10.25) \)”