The thickness at the centre of a plano convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is $2\times {10}^{8}m{s}^{-1}$ . The focal length of the lens is ___.

If we assume ‘R’ be the radius of curvature of curved surface then 
$\begin{array}{l}(R-t{)}^2+3^2=R^2\\ \Rightarrow (R-(0.3){)}^2+3^2=R^2\\ \Rightarrow R^2+(0.3{)}^2-2R(0.3)+9=R^2\\ \Rightarrow 0.09-0.6R+9=0\\ \Rightarrow R=15.15\mathrm{cm}\end{array}$ 
Refractive index of the lens material 
$\begin{array}{l}\mu =\frac{C_0}{C}=\frac{3\times {10}^8}{2\times {10}^8}=3/2\\ \frac{1}{f}=(\mu -1)\left(\frac{1}{R}-\frac{1}{\mathrm{\infty }}\right)\\ \Rightarrow \frac{1}{f}=\left(\frac{3}{2}-1\right)\left(\frac{1}{15}-0\right)=\frac{1}{30}\\ \Rightarrow f=30cm\end{array}$