$A$ 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:

$A$ needle is lying at the bottom of a water tank of height $12 \,cm$. The apparent depth of the needle measured by a microscope is $9 \,cm$. If the water is replaced by a liquid of refractive index of $1.5$ of same height, the distance through which the microscope has to be moved to focus the needle again is (in $\,cm$)

The refractive index of water with respect to air is $4/3$ and the refractive index of glass with respect to air is $3/2$. The refractive index of water with respect to glass is

If the velocity of light in the first medium is $v_1$ and in the second medium is $v_2$,then the refractive index of the second medium with respect to the first medium is given by:

In a medium,the speed of a light wave decreases to $0.2$ times its speed in free space. The ratio of relative permittivity to the refractive index of the medium is $x: 1$. The value of $x$ is $...........$ (Given: speed of light in free space $= 3 \times 10^8 \ m \ s^{-1}$ and for the given medium $\mu_r = 1$)

Monochromatic light of wavelength $589 \; nm$ is incident from air on a water surface. What are the wavelength,frequency,and speed of
$(a)$ reflected,and
$(b)$ refracted light? Refractive index of water is $1.33$.