$A$ bird is flying $3\, m$ above the surface of water. If the bird is diving vertically down with speed $= 6\, m/s$,its apparent velocity as seen by a stationary fish underwater is $m/s$.

$A$ small pin fixed on a table top is viewed from above from a distance of $50 \, cm$. By what distance would the pin appear to be raised if it is viewed from the same point through a $15 \, cm$ thick glass slab held parallel to the table? (Refractive index of glass $= 1.5$)

Obtain the relation between the real depth and apparent depth of the bottom of a tank filled with water when observed from air.

$A$ rectangular tank of depth $8 \, m$ is full of water $(\mu = 4/3)$. The bottom is seen at an apparent depth of:

Mention the relation between the real depth and the apparent depth in terms of the refractive indices of the media.

$A$ bubble in a glass slab (refractive index $1.5$) when viewed from one side appears at $5 \,cm$ and at $2 \,cm$ from the other side. Then the thickness of the slab is: (in $\,cm$)