$A$ magician during a show makes a glass lens with $n = 1.47$ disappear in a trough of liquid. What is the refractive index of the liquid? Could the liquid be water?

$A$ red colour in air has a wavelength of $760 \,nm$. When light passes through water of refractive index $n = \frac{4}{3}$,its wavelength becomes $570 \,nm$. (The wavelength of yellow colour in air is $570 \,nm$). The colour of the red light in water is:

The difference of speed of light in the two media $A$ and $B$ $(v_{A}-v_{B})$ is $2.6 \times 10^{7} \, m/s$. If the refractive index of medium $B$ is $1.47$,then the ratio of refractive index of medium $B$ to medium $A$ is: (Given: speed of light in vacuum $c = 3 \times 10^{8} \, m/s$)

$A$ monochromatic light wave with wavelength $\lambda_1$ and frequency $v_1$ in air enters another medium. If the angle of incidence and angle of refraction at the interface are $45^{\circ}$ and $30^{\circ}$ respectively,then the wavelength $\lambda_2$ and frequency $v_2$ of the refracted wave are :

$A$ ray of light travelling through glass of refractive index $\sqrt{2}$ is incident on a glass-air boundary at an angle of incidence of $45^{\circ}$. If the refractive index of air is $1$,then the angle of refraction will be: $[\sin 45^{\circ} = \frac{1}{\sqrt{2}}, \sin 90^{\circ} = 1]$ (in $^{\circ}$)

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: