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.

Immiscible transparent liquids $A, B, C, D$ and $E$ are placed in a rectangular glass container,forming layers based on their densities. The refractive indices of the liquids are given in the table below. The container is illuminated from the side,and a small piece of glass with a refractive index of $1.61$ is gently dropped into the liquid layers. In which liquid will the glass piece not be visible as it descends?
| Liquid | Refractive Index |
| :--- | :--- |
| $A$ | $1.51$ |
| $B$ | $1.53$ |
| $C$ | $1.61$ |
| $D$ | $1.52$ |
| $E$ | $1.65$ |

$A$ transparent slab of thickness $d$ has a refractive index $n(z)$ that increases with $z$. Here $z$ is the vertical distance inside the slab,measured from the top. The slab is placed between two media with uniform refractive indices $n_1$ and $n_2 (> n_1)$,as shown in the figure. $A$ ray of light is incident with angle $\theta_i$ from medium $1$ and emerges in medium $2$ with refraction angle $\theta_f$ with a lateral displacement $l$. Which of the following statement$(s)$ is(are) true?
$(A)$ $n_1 \sin \theta_i = n_2 \sin \theta_f$
$(B)$ $n_1 \sin \theta_i = (n_2 - n_1) \sin \theta_f$
$(C)$ $l$ is independent of $n_2$
$(D)$ $l$ is dependent on $n(z)$

When light enters from air to water,then its

The angle of incidence is found to be twice the angle of refraction when a ray of light passes from vacuum into a medium of refractive index $\mu$. The angle of incidence will be

$A$ ray of light is incident on a transparent sphere at an angle of $\pi / 4$ and is refracted at an angle $r$. The ray emerges from the sphere after suffering one internal reflection. The total angle of deviation of the ray is