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:

$A$ small pin fixed on a table top is viewed from above from a distance of $100 \ cm$. By what distance would the pin appear to be raised if it is viewed from the same point through a $9 \ cm$ thick glass slab held parallel to the table (in $cm$)? The refractive index of glass is $1.5$.

$A$ monochromatic ray of light travels through a glass slab and a water column. The number of waves in a glass slab of thickness $4 \,cm$ is the same as in a water column of height $5 \,cm$. If the refractive index of glass is $\frac{5}{3}$, then the refractive index of water is:

An underwater swimmer is at a depth of $12 \, m$ below the surface of water. $A$ bird is at a height of $18 \, m$ from the surface of water,directly above his eyes. For the swimmer,the bird appears to be at a distance from the surface of water equal to ....... $m$ (Refractive index of water is $4/3$).

$A$ vessel of depth $x$ is half filled with oil of refractive index $\mu_1$ and the other half is filled with water of refractive index $\mu_2$. The apparent depth of the vessel when viewed from above is

$A$ glass slab of thickness $3 \, cm$ and refractive index $3/2$ is placed on an ink mark on a piece of paper. For a person looking at the mark from a distance of $5.0 \, cm$ above the slab,the distance of the mark will appear to be.....$cm$.