Question

A telescope has an objective lens of diameter 10cmand is situated at a distance of 1 kilometre from two objects. The minimum distance between the two objects which can be resolved by the telescope when the mean wavelength of light is 5000 angstrom is of the order how much?

Answer 1

$$\begin{gathered} Thepowerofresolutionofthetelescopeisgivenby: \\ ∆\theta \approx \frac{1.22\lambda }{2a} \\ where,a=radiusofthelense \\ therefore, \\ ∆\theta =\frac{1.22\times 5000\times {10}^{-10}}{10\times {10}^{-2}}(sincethediameterisgiveinthequestion) \\ ∆\theta =6.1\times {10}^{-6}radians \\ Now, \\ ∆\theta =\frac{arc}{radius}=\frac{minimumdis\tan cebetweenthetwopoints}{dis\tan cebetweenthetelescopeandthelocationoftwopoints} \\ 6.1\times {10}^{-6}=\frac{minimumdistancebetweenthetwopoints}{{10}^3} \\ minimumdistancebetweenthetwopoints=6.1\times {10}^{-3}m \\ 6.1\times {10}^{-3}mistheminimumdis\tan cethatthetelescopewillbeabletoresolveatthatdis\tan ce. \end{gathered}$$