A refracting telescope has an objective of focal length `1 m` and an eye piece of focal length `20 cm`. The final image of the sun `10 cm` in diameter is formed at a distance of `24 cm` from eye piece. What angle does the sun subtend at the objective ?

Answer

`0.0455 rad`

Explanation

Here, `f_(0) = 1 m = 100 cm, f_(e) = 20 cm`.
If `h_(1) =` size of image formed by objective lens and `h_(2) =` size of image formed by eye piece
`tan alpha = (h_(1))/(f_(0)) = (h_(1))/(100)`
`m_(e) = (h_(2))/(h_(1)) = 1 + (d)/(f_(e))`
`(10)/(h_(1)) = 1 + (24)/(20) = (44)/(20) h_(1) = (200)/(44) = (50)/(11) cm`
`alpha ~= tan alpha = (h_(1))/(100) = (50)/(1100) = (1)/(22)rad = 0.0455 rad`