The refractive indices of glass and water with respect to air are $3/2$ and $4/3$ respectively. The refractive index of glass with respect to water will be

$A$ red colour in air has a wavelength of $760 \,nm$. When light passes through water of refractive index $n = \frac{4}{3}$,its wavelength becomes $570 \,nm$. (The wavelength of yellow colour in air is $570 \,nm$). The colour of the red light in water is:

If the angle of incidence is twice the angle of refraction in a medium of refractive index $\mu$,then the angle of incidence is

$A$ tank is filled with water to a height of $12.5 \;cm$. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be $9.4 \;cm$. What is the refractive index of water?
If water is replaced by a liquid of refractive index $1.63$ up to the same height,by what distance would the microscope have to be moved to focus on the needle again?

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.

An electromagnetic wave of wavelength $\lambda_0$ (in vacuum) passes from $P$ towards $Q$ crossing three different media of refractive index $\mu, 2\mu$ and $3\mu$ respectively as shown in the figure. Let $\phi_P$ and $\phi_Q$ be the phase of the wave at points $P$ and $Q$. Find the phase difference $\phi_Q - \phi_P$. [Take: $\mu = 1$]