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 $c=3\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}$)

An object '$O$' is placed at a distance of $100 \mathrm{cm}$ in front of a concave mirror of radius of curvature $200 \mathrm{cm}$ as shown in the figure. The object starts moving towards the mirror at a speed $2 \mathrm{cm} {\mathrm{s}}^{-1}$. The position of the image from the mirror after $10 \mathrm{s}$ will be at _____ $\mathrm{cm}$.