White light is incident normally on a glass slab. Inside the glass slab,

Two transparent slabs have the same thickness $t$. One is made of material $X$ of refractive index $1.5$. The other is made of two materials $Y$ and $Z$ having thicknesses in the ratio $1 : 2$. The refractive index of $Z$ is $1.6$. If a monochromatic parallel beam passing through the slabs has the same number of wavelengths inside both,the refractive index of $Y$ is

$A$ bird is flying $3\, m$ above the surface of water. If the bird is diving vertically down with speed $= 6\, m/s$,its apparent velocity as seen by a stationary fish underwater is $m/s$.

Time taken by the sunlight to pass through a slab of $4 \ cm$ and refractive index $1.5$ is . . . . . . $s$.

When a convex lens is placed above an empty tank, the image of a mark at the bottom of the tank, which is $45 \ cm$ from the lens, is formed $36 \ cm$ above the lens. When a liquid is poured in the tank to a depth of $40 \ cm$, the distance of the image of the mark above the lens is $48 \ cm$. The refractive index of the liquid is

The image of point $P$ when viewed from the top of the slabs will be: