Light is incident normally on face $AB$ of a prism as shown in the figure. $A$ liquid of refractive index $\mu$ is placed on face $AC$ of the prism. The prism is made of glass of refractive index $\frac{3}{2}$. The limit of $\mu$ for which total internal reflection takes place on face $AC$ is

White light is incident on the interface of glass and air as shown in the figure. If green light is just totally internally reflected,then the emerging ray in air contains:

Write the definition of critical 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:
$(A)$ $\frac{NA_1 NA_2}{NA_1+NA_2}$ $(B)$ $NA_1+NA_2$ $(C)$ $NA_1$ $(D)$ $NA_2$

When a ray of light emerges from a block of glass,the critical angle is

Initially,$AB$ is the interface of a slab of refractive index $\mu$ and air. $A$ ray of light strikes $AB$ at the critical angle $\theta_c$. Now,a slab $ABCD$ of refractive index $\mu_1$ is placed on top such that total internal reflection takes place at the surface $CD$ (and not at the surface $AB$). What should be the value of $\mu_1$?