The graph between the sine of the angle of refraction $(\sin r)$ in medium $2$ and the sine of the angle of incidence $(\sin i)$ in medium $1$ is shown below. Based on this,which of the following statements is correct? (Given: $\tan 36^o \approx \frac{3}{4}$)

$A$ glass prism of refractive index $1.5$ is immersed in water (refractive index $\frac{4}{3}$) as shown in the figure. $A$ light beam incident normally on the face $AB$ is totally internally reflected at the face $AC$ to reach the face $BC$,if:

$A$ diver at a depth of $12 \ m$ in water $(\mu = 4/3)$ sees the sky in a cone of semi-vertical angle:

Light guidance in an optical fiber can be understood by considering a structure comprising of a thin solid glass cylinder of refractive index $n_1$ surrounded by a medium of lower refractive index $n_2$. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media $n_1$ and $n_2$. All rays with the angle of incidence $i$ less than a particular value $i_m$ are confined in the medium of refractive index $n_1$. The numerical aperture $(NA)$ of the structure is defined as $\sin i_m$.
$1.$ For two structures namely $S_1$ with $n_1=\sqrt{45}/4$ and $n_2=3/2$,and $S_2$ with $n_1=8/5$ and $n_2=7/5$,and taking the refractive index of water to be $4/3$ and that of air to be $1$,the correct option$(s)$ is(are):
$(A)$ $NA$ of $S_1$ immersed in water is the same as that of $S_2$ immersed in a liquid of refractive index $\frac{16}{3\sqrt{15}}$
$(B)$ $NA$ of $S_1$ immersed in a liquid of refractive index $\frac{6}{\sqrt{15}}$ is the same as that of $S_2$ immersed in water
$(C)$ $NA$ of $S_1$ placed in air is the same as that of $S_2$ immersed in a liquid of refractive index $\frac{4}{\sqrt{15}}$
$(D)$ $NA$ of $S_1$ placed in air is the same as that of $S_2$ placed in water
$2.$ If two structures of the same cross-sectional area,but different numerical apertures $NA_1$ and $NA_2$ $(NA_2 < NA_1)$ are joined longitudinally,the numerical aperture of the combined structure is:
$(A)$ $\frac{NA_1 NA_2}{NA_1+NA_2}$ $(B)$ $NA_1+NA_2$ $(C)$ $NA_1$ $(D)$ $NA_2$

$A$ light wave enters from medium $1$ to medium $2$. Its velocity in the $2^{nd}$ medium is double that in the $1^{st}$ medium. For total internal reflection,the angle of incidence must be greater than.......$^o$.

Assertion : In optical fibre,the diameter of the core is kept small.
Reason : This smaller diameter of the core ensures that the fibre should have incident angle more than the critical angle required for total internal reflection.