Blue light travelling in a vacuum has a wavelength of $450 \ nm$. It enters a medium whose refractive index is $1.5$. What is its frequency in the medium? $(Speed of light in vacuum = 3 \times 10^8 \ m \ s^{-1})$

$A$ light ray passes through four transparent media with refractive indices $\mu_1, \mu_2, \mu_3$ and $\mu_4$ as shown in the figure. All surfaces are parallel to each other. If the emergent ray $CD$ is parallel to the incident ray $AB$,then:

$A$ light ray is incident on a glass slab at an angle of incidence of $60^o$. If the angle between the reflected ray and the refracted ray is $90^o$,what is the refractive index of the glass slab?

Light of wavelength $\lambda$ in air enters a medium of refractive index $\mu$. Two points in this medium,lying along the path of this light,are at a distance $x$ apart. The phase difference between these points 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 $\,cm$)

$A$ light ray enters a solid glass sphere of refractive index $\mu=\sqrt{3}$ at an angle of incidence $60^{\circ}$. The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is......