Answer to Question #94714 in Optics for Vinay mony

Question

"the diameter of after 8 th dark ring is reflected system 4×10^-3m. find radius of curvature of the plano-convex lens used, if the wavelength of light is 589×10^-9 m"?

Answer 1

For the convex-plane lens system, nth dark ring have the diameter, which can be determined by:

$$r_n=\sqrt{nR\lambda}$$

So, the radius of curvature is:

$$R=\frac{r_n^2}{n\lambda}=\frac{d_n^2}{4n\lambda}=\frac{(4*10^{-3})^2}{4*8*589*10^{-9}}=0.85m$$