The limit of resolution of a telescope is `2.5xx10^(-7)` rad. If the telescope is used to detect light of wavelength 500 nm coming from a star, the diameter of the objective lens used by telescope is

Options

A. 244 cm
B. 258 cm
C. 228 cm
D. 264 cm

Answer

A

Explanation

Given, limit of resolution, `alpha=2.5xx10^(-7)` rad.
and wavelength, `lambda=500` nm
As, limit of resolution of a telescope,
`alpha=(1.22lambda)/(a)`
So, `a=(1.22 lambda)/(alpha)=(1.22xx500xx10^(-9))/(2.5xx10^(-7))`
`rArr a=2.44 m`
`=244` cm
Hence, the correct option is (a).