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

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

There is a small source of light at some depth below the surface of water (refractive index $= 4/3$) in a tank of large cross-sectional surface area. Neglecting any reflection from the bottom and absorption by water,the percentage of light that emerges out of the surface is (nearly) ..........$\%$. [Use the fact that the solid angle subtended by a cone of semi-vertical angle $\theta$ is $\Omega = 2\pi(1 - \cos\theta)$]

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

$A$ cut diamond sparkles because of its

$A$ water-proof laser pointer of length $10 \,cm$ is placed in a water tank. It rotates about a horizontal axis passing through its centre of mass in a vertical plane as shown in the figure. The time period of rotation is $60 \,s$. Assuming the water to be still and no reflections from the surface of the tank, the duration for which the light beam escapes the tank in one time period is close to ............. $s$. (Take, refractive index of water $= 1.33$)