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 prop = (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`
`prop ~= tan prop = (h_1)/(100) = (50)/(1100) = (1)/(2) rad = 0.0455 rad`.