Time taken by light to travel in two different materials $A$ and $B$ of refractive indices ${\mu }_A$ and ${\mu }_B$ of same thickness is $t_1$ and $t_2$ respectively. If $t_2-t_1=5\times {10}^{-10}\mathrm{s}$ and the ratio of ${\mu }_A$ to ${\mu }_B$ is $1:2$. Then the thickness of material, in meter is: (Given $v_A$ and $v_B$ are velocities of light in $A$ and $B$ materials respectively).

The graph between $\frac{1}{u}$ and $\frac{1}{v}$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of lens is $1.5$ and its both the surfaces have same radius of curvatures $R$. The value of $R$ will be _____ $\mathrm{cm}$.

(Where $u=$ object distance, $v=$ image distance)

In the given figure, the face $AC$ of the equilateral prism is immersed in a liquid of refractive index $n$. For incident angle $60°$ at the side $AC$, the refracted light beam just grazes along face $AC$. The refractive index of the liquid $n=\frac{\sqrt{x}}{4}$. The value of $x$ is _____ .
(Given refractive index of glass $=1.5$)

A thin prism of angle $6°$ and refractive index for yellow light $\left(n_{\mathrm{Y}}\right)1.5$ is combined with another prism of angle $5°$ and $n_{\mathrm{Y}}=1.55$. The combination produces no dispersion. The net average deviation $\left(\delta \right)$ produced by the combination is ${\left(\frac{1}{x}\right)}^{°}$. The value of $x$ is _____ .

As shown in the figure, after passing through the medium $1$. The speed of light $v_2$ in medium $2$ will be :
(Given $c=3\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}$)