Captain Jack Sparrow tries to observe a fish almost vertically below him in a magical sea of variable refractive index $\mu = y^2 + 1$,where $y$ is the depth below the water surface. Find the apparent depth of the fish below the water level as seen by Captain Jack Sparrow. The actual depth of the fish is $1 \ m$.

$A$ magician during a show makes a glass lens with $n = 1.47$ disappear in a trough of liquid. What is the refractive index of the liquid? Could the liquid be water?

$A$ tank is filled with benzene to a height of $120 \,mm$. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be $80 \,mm$. The refractive index of benzene is: (in $.5$)

An observer can see through a small hole on the side of a jar (radius $15\, cm$) at a point at a height of $15\, cm$ from the bottom (see figure). The hole is at a height of $45\, cm$. When the jar is filled with a liquid up to a height of $30\, cm$,the same observer can see the edge at the bottom of the jar. If the refractive index of the liquid is $N/100$,where $N$ is an integer,the value of $N$ is $.....$

$A$ boat has a green light of wavelength $\lambda = 500 \ nm$ on the mast. What wavelength would be measured and what colour would be observed for this light as seen by a diver submerged in water by the side of the boat? Given,$n_{w} = 4/3$.

The optical path of a particular ray of light that has travelled a distance of $3 \ cm$ in flint glass is the same as that of a ray travelling a distance of '$x$' $cm$ through another medium. The value of '$x$' is [refractive index of flint glass $= 1.6$, refractive index of another medium $= 1.25$]. (in $cm$)