The radii of curvature of the faces of a double-convex lens are $\displaystyle 20$ cm and $\displaystyle 30$ cm . Its power is $\displaystyle \frac{25}{6} \mathrm{D}$. What is the refractive index of the glass of the lens?

\(\displaystyle \mathrm{R}_{1}=20 \mathrm{~cm}, \mathrm{R}_{2}=-30 \mathrm{~cm} \quad \mathrm{P}=\frac{25}{6} \mathrm{D}=\frac{25}{600} c m^{-1}\) \(\displaystyle \mathrm{P}=(\mathrm{n}-1)\left(\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right)\) \(\displaystyle \frac{25}{600}=(\mathrm{n}-1)\left(\frac{1}{20}+\frac{1}{30}\right)\) \(\displaystyle \frac{25}{600}=(\mathrm{n}-1)\left(\frac{50}{20 \times 30}\right)\) \(\displaystyle 25=(\mathrm{n}-1) 50\) \(\displaystyle \mathrm{n}-1=\frac{1}{2}\) \(\displaystyle \mathrm{n}=\frac{3}{2}\)