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

$\begin{array}{l}Refractive Index, \\ n=\frac{3}{2}[\because n=\frac{c}{v}]\\ Apply pythagoras theorem, \\ 3^2+{(R-0.3)}^2=R^2 (all dimensions are in cm)\\ \Rightarrow R=15cm\\ Apply Lens Maker formula, \\ \therefore \frac{1}{f}=(\frac{3}{2}-1)\left(\frac{1}{15}\right)\\ \begin{array}{l}\left[\because \frac{1}{f}=(n-1)(\frac{1}{R_1}-\frac{1}{R_2}) and{R}_1=\infty R_2=-15\right]\\ \end{array}\\ \Rightarrow f=30cm\end{array}$