An ice cube has a bubble inside. When viewed from one side,the apparent distance of the bubble is $12 \ cm$. When viewed from the opposite side,the apparent distance of the bubble is observed as $4 \ cm$. If the side of the ice cube is $24 \ cm$,the refractive index of the ice cube is $.....$.

$A$ monochromatic light wave is incident normally on a glass slab of thickness $d$,as shown in the figure. The refractive index of the slab increases linearly from $n_1$ to $n_2$ over the height $h$. Which of the following statement$(s)$ is (are) true about the light wave emerging out of the slab?

As shown in the figure,a plane mirror is fixed at a height of $50\,cm$ from the bottom of a tank containing water $\left(\mu = \frac{4}{3}\right)$. The height of water in the tank is $8\,cm$. $A$ small bulb is placed at the bottom of the water tank. The distance of the image of the bulb formed by the mirror from the bottom of the tank is $......\,cm$.

When a convex lens is placed above an empty tank,the image of a mark at the bottom of the tank,which is $45 \ cm$ from the lens,is formed $36 \ cm$ above the lens. When a liquid is poured in the tank to a depth of $40 \ cm$,the distance of the image of the mark above the lens is $48 \ cm$. The refractive index of the liquid is

$A$ printed page is kept pressed by a transparent cube of edge $t$. The refractive index of the cube varies as $\mu(z) = 1 + \frac{z}{t}$,where $z$ is the vertical distance from the bottom of the cube. If viewed from the top,then the printed letters appear to be shifted by an amount

$A$ glass slab of thickness $3 \ cm$ is placed on an ink mark on a piece of paper. For a person looking at the mark from a distance of $5.0 \ cm$ above the top surface of the slab, the mark appears to be at a distance of $4.0 \ cm$ from the observer. The refractive index of the slab is: