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:

The lower half of a vessel of depth $2d \text{ cm}$ is filled with a liquid of refractive index $\mu_1$ and the upper half with a liquid of refractive index $\mu_2$. The apparent depth of the vessel seen perpendicularly is

An air bubble in a glass slab $(\mu = 1.5)$ appears to be $5 \, cm$ deep when viewed through one face and $2 \, cm$ deep when viewed through the opposite face. What is the thickness of the slab in $cm$?

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

Two parallel rays of red and violet colour pass through a glass slab. Which of the following is correct?

An air bubble in a glass slab $(\mu = 1.5)$ is $5 \, cm$ deep when viewed from one face and $2 \, cm$ deep when viewed from the opposite face. The thickness of the slab is......$cm$