The critical angle of a medium with respect to air is $45^o$. The refractive index of the medium is

As shown in the figure,a light ray $P$ enters a slab at an angle of $60^{\circ}$ with the normal. Inside the slab,the light ray $Q$ undergoes total internal reflection at the vertical face. Find the minimum refractive index of the slab.

If light travels a distance $x$ in time $t_1$ sec in air and $10x$ distance in time $t_2$ sec in a certain medium,then find the critical angle of the medium.

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 ${\sin ^{ - 1}}\left( {\frac{{\sin {i_A}}}{{\sin {i_B}}}} \right)$.

In an optical fibre, the core and cladding are made with materials of refractive indices $1.5$ and $1.414$ respectively. To observe total internal reflection, what will be the range of the incident angle with the axis of the optical fibre?

$A$ light wave travelling linearly in a medium of dielectric constant $4$ is incident on the horizontal interface separating the medium from air. The angle of incidence for which the total intensity of the incident wave will be reflected back into the same medium is (Given: relative permeability of the medium $\mu_{r} = 1$) (in $^{\circ}$)