Calculate the separation of two points on moon that can be resolved using 600 cm telescope. Given distance of moon from earth = \( 3.8\times10^{10}\,\mathrm{cm} \). The wavelength most sensitive to eye is \( 5.5\times10^{-5}\,\mathrm{cm} \).
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4180 cm
The smallest angular separation that a telescope of aperture a can resolve is \( \Delta\theta \approx 1.22\lambda/a \). Two points on the Moon, a distance D away, are just resolved when their separation is \( \Delta x = D\,\Delta\theta \).
Keep every length in centimetres, as the data are given.
\( \displaystyle \Delta x = \frac{1.22\,\lambda D}{a} \)
Taking the factor 1.22 as 1.2:
\( \displaystyle \Delta x = \frac{1.2\times5.5\times10^{-5}\times3.8\times10^{10}}{600}\,\mathrm{cm} \)
\( \Delta x \approx 4180\,\mathrm{cm} \)
With the exact factor 1.22 the value is about 4250 cm, which is again closest to Option (1).