$A$ fish inside water sees the outside world through a circular horizon. If the refractive index of water is $4/3$ and the fish is $12 \, cm$ below the water surface,then the radius of this circle is $= ..... cm$.

Let the refractive index of a denser medium with respect to a rarer medium be $n_{12}$ and its critical angle be $\theta_C$. At an angle of incidence $A$ when light is travelling from a denser medium to a rarer medium,a part of the light is reflected and the rest is refracted,and the angle between the reflected and refracted rays is $90^o$. Angle $A$ is given by

In the figure shown,for an angle of incidence $45^{\circ}$ at the top surface,what is the minimum refractive index $\mu$ needed for total internal reflection at the vertical face?

$A$ prism has a refractive index of $1.5$. If a light ray undergoes total internal reflection at the interface with a liquid,what is the maximum possible refractive index of the liquid? (Refer to the provided diagram for geometry).

$A$ ray is incident from a medium of refractive index $2$ into a medium of refractive index $1$. The critical angle is (in $^{\circ}$)

$A$ beam of light consists of red,green,and blue colors. It is incident on the $AB$ face of a right-angled prism as shown in the figure. The refractive indices for red,green,and blue colors are $1.39$,$1.44$,and $1.47$ respectively. What will a person see when looking at the $AC$ surface of the prism?