$A$ glass prism of refractive index $1.5$ is immersed in water (refractive index $4/3$). $A$ light beam incident normally on the face $AB$ is totally reflected to reach the face $BC$ if

$A$ 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 $^{\circ}$)

The critical angle of light going from medium $x$ to medium $y$ is $\theta$. The speed of light in medium $x$ is $v$. The speed of light in medium $y$ is:

On a bright sunny day,a diver of height $h$ stands at the bottom of a lake of depth $H$. Looking upward,he can see objects outside the lake in a circular region of radius $R$. Beyond this circle,he sees the images of objects lying on the floor of the lake. If the refractive index of water is $4/3$,then the value of $R$ is:

If the critical angle for a material to air is $30^o$,the refractive index of the material will be

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