Refraction Questions

An electromagnetic wave of frequency $\nu =3.0\text{MHz}$ passes from vacuum into a dielectric medium with permittivity $ϵ=4.0{ϵ}_0$. Then:

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

A thin glass (refractive index $1.5$) lens has optical power of $-5\text{D}$ in air. Its optical power in a liquid medium with refractive index $1.6$ will be:

A transparent solid cylindrical rod has a refractive index of $\frac{2}{\sqrt{3}}$. It is surrounded by air. A light ray is incident at the mid point of one end of the rod. The incident angle $\theta$ for which the light ray grazes along the wall of the rod is:

An initially parallel cylindrical beam travels in a medium of refractive index $\mu (I)={\mu }_0+{\mu }_{2}I$, where ${\mu }_0$ and ${\mu }_2$ are positive constants and $I$ is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. As the beam enters the medium, it will:

An initially parallel cylindrical beam travels in a medium of refractive index $\mu (I)={\mu }_0+{\mu }_{2}I$. The speed of light in the medium is:

Let the $x-z$ plane be the boundary between two transparent media. Medium 1 in $z\ge 0$ has a refractive index of $\sqrt{2}$ and medium 2 with $z<0$ has a refractive index of $\sqrt{3}$. A ray of light in medium 1 given by the vector $\vec{A}=6\sqrt{3}\hat{i}+8\sqrt{3}\hat{j}-10\hat{k}$ is incident on the plane of separation. The angle of refraction in medium 2 is:

An object $2.4\text{m}$ in front of a lens forms a sharp image on a film $12\text{cm}$ behind the lens. A glass plate $1\text{cm}$ thick, of refractive index $1.50$ is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object be shifted to be in sharp focus on film?