When a light ray enters from air into water, which of the following properties does not change?

$A$ cubical vessel has opaque walls. An observer is located such that she can see only the wall $CD$,but not the bottom. To what height (in $cm$) should water be poured so that she can see an object placed at the bottom at a distance of $10 \, cm$ from the corner $C$? The refractive index of water is $\mu = 1.33 \approx 4/3$.

On a glass plate,a light wave is incident at an angle of $60^o$. If the reflected and the refracted waves are mutually perpendicular,the refractive index of the material is:

Most materials have a refractive index,$n > 1$. So,when a light ray from air enters a naturally occurring material,then by Snell's law,$\frac{\sin \theta_1}{\sin \theta_2} = \frac{n_2}{n_1}$,it is understood that the refracted ray bends towards the normal. But it never emerges on the same side of the normal as the incident ray. According to electromagnetism,the refractive index of the medium is given by the relation,$n = \left(\frac{c}{v}\right) = \pm \sqrt{\varepsilon_r \mu_r}$. Where $\varepsilon_r$ and $\mu_r$ are negative,one must choose the negative root of $n$. Such negative refractive index materials can now be artificially prepared and are called meta-materials. They exhibit significantly different optical behavior,without violating any physical laws. Since $n$ is negative,it results in a change in the direction of propagation of the refracted light. However,similar to normal materials,the frequency of light remains unchanged upon refraction even in meta-materials.
$1.$ Choose the correct statement.
$(A)$ The speed of light in the meta-material is $v = c|n|$.
$(B)$ The speed of light in the meta-material is $v = \frac{c}{|n|}$.
$(C)$ The speed of light in the meta-material is $v = c$.
$(D)$ The wavelength of the light in the meta-material $(\lambda_m)$ is given by $\lambda_m = \frac{\lambda_{\text{air}}}{|n|}$,where $\lambda_{\text{air}}$ is the wavelength of the light in air.
$2.$ For light incident from air on a meta-material,the appropriate ray diagram is:

$A$ beam of white light is partially reflected and partially refracted from a surface. The angle between the reflected and refracted light is $90^{\circ}$. The angle of refraction is $30^{\circ}$. The angle of incidence must be (in $^{\circ}$)

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.