On a glass plate,a light wave is incident at an angle of $60^o$. If the reflected and the refracted waves are mutually perpendicular,the refractive index of the material is:

When a light ray enters a medium with refractive index $\mu$,it is observed that the angle of refraction is half the angle of incidence. The angle of incidence is .........

$A$ ray of light travels from air to water to glass and again from glass to air. The refractive index of water with respect to air is '$X$', glass with respect to water is '$Y$', and air with respect to glass is '$Z$'. Which one of the following is correct?

$A$ ray of light is incident at $30^{\circ}$ from a medium of refractive index $2$ into a medium of refractive index $1$. The angle of refraction is: (in $^{\circ}$)

$A$ girl standing at point $P$ on a beach wishes to reach a point $Q$ in the sea as quickly as possible. She can run at $6 \, kmh^{-1}$ on the beach and swim at $4 \, kmh^{-1}$ in the sea. She should take the path

$A$ 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: