Question

While building your first telescope, your nerd friend suggested a brilliant idea for you to try and replace the reflecting mirror of the telescope by a fisk of mercury rotating about a vertical axis with some angular velocity w that forms a spherical surface of radius R, in such a telescope, the the focal length of the telescope would be function of the rotating speed of the mercury disk, calculate how much angular velocity is needed for the telescope to have a focal length of 15 cm?

Answer 1

Focal length of the telescope (f)=15cm

So, radius of the curved surface $(R)=2f = 30cm$

Angular velocity $(V)= R\omega$

Or we can write it as $(R)=\frac{V}{\omega}$

$\Rightarrow 2f= \frac{V}{\omega}$

$\Rightarrow 30=\frac{V}{\omega}$