The time taken by sunlight to cross a $5 \,mm$ thick glass plate $(\mu = 3/2)$ is

Consider the situation shown in the figure. Water $\left( \mu_w = \frac{4}{3} \right)$ is filled in a beaker up to a height of $10 \, cm$. $A$ plane mirror is fixed at a height of $5 \, cm$ from the surface of the water. The distance of the image from the mirror after reflection of an object $O$ at the bottom of the beaker is......$cm$.

$A$ narrow,paraxial beam of light is converging towards a point $I$ on a screen. $A$ plane parallel plate of glass of thickness $t$ and refractive index $\mu$ is introduced in the path of the beam. The convergence point is shifted by

An object lying $100 \ cm$ inside water is viewed normally from air. If the refractive index of water is $\frac{4}{3}$,then the apparent depth of the object is (in $cm$)

$A$ ray of light is incident on one face of a transparent slab of thickness $15 \, cm$. The angle of incidence is $60^{\circ}$. If the lateral displacement of the ray on emerging from the parallel plane is $5\sqrt{3} \, cm$,the refractive index of the material of the slab is:

$A$ convex lens with lateral magnification $2$ is used to image a point at the bottom of a tank. The image of the point is formed $60 \ cm$ above the lens. Now a liquid is filled into the tank to a height of $24 \ cm$. It is found that the distance of the image of the same point is now $120 \ cm$ above the lens. Find the refractive index of the liquid.