Mirror in the arrangement shown in figure is moving up with speed $4 cm/sec$. Find the speed of final image of object O (in cm/s) formed after two refraction and one reflection.
 

Distance of object from free surface = x
Distance of first image from free Surface =  $\mu x$
Distance of first image from free Mirror =  $(\mu x+y)$
Distance of Secondary image from free mirror = $(\mu x+y)$
Distance of Secondary image from free Surface =  $(\mu x+2y)$
Distance of Third image from free Surface =  $\frac{(\mu x+2y)}{\mu } = x+\frac{2y}{\mu }$
Speed of image =  $\frac{d}{dt}(x+\frac{2y}{\mu })=\frac{2}{\mu }\frac{dy}{dt}=2x\frac{3}{4}x4=6cm/s$