$A$ printed page is pressed by a glass of water. The refractive index of the glass and water is $1.5$ and $1.33$,respectively. If the thickness of the bottom of the glass is $1\, cm$ and the depth of the water is $5\, cm$,how much will the page appear to be shifted if viewed from the top (in $,cm$)?

How much water should be filled in a container $21 \ cm$ in height,so that it appears half-filled when viewed from the top of the container? (Given that refractive index of water $\mu = 4/3$)

$A$ slab of glass,of thickness $6\, cm$ and refractive index $1.5$,is placed in front of a concave mirror,the faces of the slab being perpendicular to the principal axis of the mirror. If the radius of curvature of the mirror is $40\, cm$ and the reflected image coincides with the object,then the distance of the object from the mirror is.....$cm$

$A$ glass slab of thickness $6.0 \text{ cm}$ is placed on a piece of paper on which an ink dot is marked. By how much distance would the ink dot appear to be raised (in $\text{ cm}$)? The velocity of light in glass is $2 \times 10^8 \text{ m/s}$ and that in air is $3 \times 10^8 \text{ m/s}$.

$A$ container is filled with a liquid of refractive index $\mu_1$ up to a depth $d$ and another liquid of refractive index $\mu_2$ up to a depth $d$ is poured on top of it. What is the apparent depth of the container when viewed from above?

$A$ composite slab consisting of different media is placed in front of a concave mirror of radius of curvature $150 \, cm$. The whole arrangement is placed in water (refractive index $\mu = 4/3$). An object $O$ is placed at a distance $20 \, cm$ from the slab. The refractive indices of the different media are given in the diagram. Find the final image formed by the system.