The speed of light in media $M_{1}$ and $M_{2}$ are $1.5 \times 10^{8} \text{ m/s}$ and $2 \times 10^{8} \text{ m/s}$ respectively. $A$ ray travels from medium $M_{1}$ to the medium $M_{2}$ with an angle of incidence $\theta$. The ray suffers total internal reflection. Then the value of the angle of incidence $\theta$ is

$A$ ray of light from a denser medium strikes a rarer medium. The angle of reflection is $r$ and that of refraction is $r'$. The reflected and refracted rays make an angle of $90^{\circ}$ with each other. The critical angle will be

$A$ fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is $\frac{4}{3}$ and the fish is $12 \, cm$ below the surface,the radius of this circle in $cm$ is

$A$ point source of light $S$ is placed at the bottom of a vessel containing a liquid of refractive index $\mu = 5/3$. $A$ person is viewing the source from above the surface. There is an opaque disc $D$ of radius $r = 1\, cm$ floating on the surface of the liquid. The centre of the disc lies vertically above the source $S$. The liquid from the vessel is gradually drained out through a tap. The maximum height $h$ of the liquid for which the source cannot be seen at all from above is: (in $, cm$)

The speed of light in media $M_1$ and $M_2$ are $1.5 \times 10^8 \ m/s$ and $2.0 \times 10^8 \ m/s$ respectively. $A$ ray of light enters from medium $M_1$ to $M_2$ at an incidence angle $i$. If the ray suffers total internal reflection,the value of $i$ is

Material $A$ has a critical angle ${i_A},$ and material $B$ has a critical angle ${i_B}$ $({i_B} > {i_A})$. Then which of the following is true?
$(i)$ Light can be totally internally reflected when it passes from $B$ to $A$.
$(ii)$ Light can be totally internally reflected when it passes from $A$ to $B$.
$(iii)$ The critical angle for total internal reflection is ${i_B} - {i_A}$.
$(iv)$ The critical angle between $A$ and $B$ is ${\sin ^{ - 1}}\left( {\frac{{\sin {i_A}}}{{\sin {i_B}}}} \right)$.