b
(b) Sun is at infinity i.e. \(u = \infty \) so from mirror formula we have

\(\frac{1}{f} = \frac{1}{{ - 32}} + \frac{1}{{(- \infty )}} \Rightarrow f = - 32\)\(cm\).

When water is filled in the tank upto a height of \(20 cm,\) the image formed by the mirror will act as virtual object for water surface.

Which will form it’s image at \(I\) such that

\(\frac{{{\rm{Actual \,height}}}}{{{\rm{Apperant\, height}}}} = \frac{{{\mu _w}}}{{{\mu _a}}}\) i.e. \(\frac{{BO}}{{BI}} = \frac{{4/3}}{1}\)

\( \Rightarrow \) \(BI = BO \times \frac{3}{4}\)=\(12 \times \frac{3}{4} = 9cm\).