Answer to Question #284541 in Optics for luna

Question

Find the formula for the focal length of a thin lens if the R₂ radius of curvature

of the lens surface is k times more than R₁ radius of curvature and the refraction index of

the lens is n = 2. The medium surrounding the lens is air.

Answer 1

$$\dfrac 1f=(n-1)\bigg(\dfrac 1{R_1}-\dfrac 1{R_2}\bigg),\\\space\\ \dfrac 1f=(2-1)\bigg(\dfrac 1{R_1}-\dfrac 1{kR_1}\bigg)=\dfrac{k-1}{kR_1},\\\space\\ f=\dfrac{kR_1}{k-1}.$$