$A$ 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

The speed of light is maximum in

Electromagnetic radiation of frequency $n$,wavelength $\lambda$,travelling with velocity $v$ in air,enters a glass slab of refractive index $\mu$. The frequency,wavelength,and velocity of light in the glass slab will be respectively:

$A$ fish rising vertically up towards the surface of water with speed $3 \; ms^{-1}$ observes a bird diving vertically down towards it with speed $9 \; ms^{-1}$. The actual velocity of the bird is.......$ms^{-1}$ (Assume refractive index of water $\mu = 4/3$).

$A$ glass slab consists of thin uniform layers of progressively decreasing refractive indices $(RI)$ such that the $RI$ of any layer is $\mu - m \Delta \mu$. Here,$\mu$ and $\Delta \mu$ denote the $RI$ of the $0^{\text{th}}$ layer and the difference in $RI$ between any two consecutive layers,respectively. The integer $m = 0, 1, 2, 3, \ldots$ denotes the number of the successive layers. $A$ ray of light from the $0^{\text{th}}$ layer enters the $1^{\text{st}}$ layer at an angle of incidence of $30^{\circ}$. After undergoing the $m^{\text{th}}$ refraction,the ray emerges parallel to the interface. If $\mu = 1.5$ and $\Delta \mu = 0.015$,the value of $m$ is:

Find the refractive index of glass from the given figure,where the refractive index of water is $\mu_w = 4/3$.