$A$ beam of monochromatic light is refracted from vacuum into a medium of refractive index $1.5$. The wavelength of refracted light will be

An observer can see through a small hole on the side of a jar (radius $15\, cm$) at a point at a height of $15\, cm$ from the bottom (see figure). The hole is at a height of $45\, cm$. When the jar is filled with a liquid up to a height of $30\, cm$,the same observer can see the edge at the bottom of the jar. If the refractive index of the liquid is $N/100$,where $N$ is an integer,the value of $N$ is $.....$

An infinitely long cylinder of radius $R$ is made of an unusual exotic material with refractive index $-1$ (See figure). The cylinder is placed between two planes whose normals are along the $y$-direction. The center of the cylinder $O$ lies along the $y$-axis. $A$ narrow laser beam is directed along the $y$-direction from the lower plate. The laser source is at a horizontal distance $x$ from the diameter in the $y$-direction. Find the range of $x$ such that light emitted from the lower plane does not reach the upper plane.

$A$ parallel beam of light travels in a medium with a refractive index $\mu(I) = \mu_0 + \mu_2 I$,where $\mu_0$ and $\mu_2$ are positive constants and $I$ is the intensity. As the intensity of the light decreases,the radius of the beam increases. The speed of light in the medium is:

$A$ light ray is incident on a medium of refractive index $\mu$. The angle of incidence is twice the angle of refraction. The angle of incidence is:

$A$ large square container with thin transparent vertical walls and filled with water (refractive index $\mu = \frac{4}{3}$) is kept on a horizontal table. $A$ student holds a thin straight wire vertically inside the water at a distance of $12 \ cm$ from one of its corners,as shown in the figure. Looking at the wire from this corner,another student sees two images of the wire,located symmetrically on each side of the line of sight. The separation (in $cm$) between these images is: