Assume the situation shown in the figure. Water $(\mu_w = 4/3)$ is filled in a beaker up to a height of $10 \, cm$. $A$ plane mirror is fixed at a height of $5 \, cm$ above the water surface. The distance of the image of the object $O$ from the mirror is ...... $cm$.

$A$ microscope is focussed on a coin lying at the bottom of a beaker. The microscope is now raised up by $1 \, cm$. To what depth should the water be poured into the beaker so that the coin is again in focus? (Refractive index of water is $\frac{4}{3}$)

Two transparent slabs have the same thickness as shown. One is made of material $A$ of refractive index $1.5$. The other is made of two materials $B$ and $C$ with thickness in the ratio $1 : 2$. The refractive index of $C$ is $1.6$. If a monochromatic parallel beam passing through the slabs has the same number of waves inside both,the refractive index of $B$ is

The figure shows a transparent slab of length $1 \, m$ placed in air,whose refractive index in the $x$-direction varies as $\mu = 1 + x^2$ for $0 \leq x \leq 1$. The optical path length of ray $R$ will be:

$A$ microscope is focussed on a coin lying at the bottom of a beaker. The microscope is now raised by $1 \,cm$. To what depth should water be poured into the beaker so that the coin is again in focus is ........ $cm$ (The refractive index of water is $\frac{4}{3}$ )

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