There is a small air bubble at the centre of a solid glass sphere of radius $r$ and refractive index $\mu$. What will be the apparent distance of the bubble from the centre of the sphere, when viewed from outside?

The length of a vertical pole at the surface of a lake of water $\left(\mu = \frac{4}{3}\right)$ is $24 \, cm$. Then,to an underwater fish just below the water surface,the tip of the pole appears to be ......... $cm$ above the surface.

$A$ ray of monochromatic light is incident on the plane surface of separation between two media $X$ and $Y$ with angle of incidence $i$ in medium $X$ and angle of refraction $r$ in medium $Y$. The given graph shows the relation between $\sin i$ and $\sin r$. If $V_X$ and $V_Y$ are the velocities of the ray in media $X$ and $Y$ respectively, then which of the following is true?

The refractive indices of glass and water with respect to air are $3/2$ and $4/3$ respectively. The refractive index of glass with respect to water is:

$A$ light ray incident along a vector $\vec{AO}$ $(\vec{AO} = 2\hat{i} - 3\hat{j})$ emerges along a vector $\vec{OB}$ $(\vec{OB} = C\hat{i} - 4\hat{j})$ as shown in the figure. The value of $C$ is . . . . . . .

The $x-z$ plane separates two media $A$ and $B$ with refractive indices $\mu_1$ and $\mu_2$ respectively. $A$ ray of light travels from $A$ to $B$. Its directions in the two media are given by the unit vectors $\vec{r}_A = a\hat{i} + b\hat{j}$ and $\vec{r}_B = \alpha\hat{i} + \beta\hat{j}$ respectively,where $\hat{i}$ and $\hat{j}$ are unit vectors in the $x$ and $y$ directions. Then: