$A$ beam of light consisting of red,green and blue colours is incident on a right-angled prism on face $AB$. The refractive indices of the material for the above red,green and blue colours are $1.39, 1.44$ and $1.47$ respectively. $A$ person looking on surface $AC$ of the prism will see

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:
$(A)$ $\frac{NA_1 NA_2}{NA_1+NA_2}$ $(B)$ $NA_1+NA_2$ $(C)$ $NA_1$ $(D)$ $NA_2$

$A$ ray of light travels from a denser medium $(\mu)$ to air. The angle of incidence is denoted by $i$ and the angle of deviation by $D$. Let $C = \sin^{-1}(1/\mu)$. Which of the following graphs is correct?

$A$ rectangular glass block is placed on a printed paper lying on a horizontal surface. Find the minimum refractive index of the glass for which the letters on the paper are not visible from any of the vertical sides of the block.

$A$ point source of light is placed $4 \, cm$ below the surface of water with a refractive index of $\mu = 5/3$. What is the minimum diameter of a disc that should be placed over the source to stop all light from coming out of the water? (in $m$)

Consider a glass prism immersed in a liquid as shown below. The refractive index of glass and liquid is $1.5$ and $1.2$,respectively. $A$ ray of light enters the prism perpendicular to the face $AB$. If the ray is totally internally reflected at the face $AC$,then the largest value of angle $\theta$ is: