Question

What do you understand by the radius of curvature and center of curvature of the spherical lens?

Answer 1

Hint: First to understand we will draw a diagram representing all the parameters that are required to define the respective parameter as per the problem. The center of the spherical surface from which the lens has been cut while the radius of curvature which is the distance from the center to the surface of the lens.

Complete answer:
Here we need to define the radius of curvature and center of curvature of the spherical lens. Below diagram shows the required parameters:

Where in this diagram $C$ represents the center of curvature of the respective sphere.

Center of Curvature: From the center of curvature we understand that it is the center of the sphere that is a part of a lens. Since we know that the concave and the convex lens are formed by the combination of two parts of the sphere that are represented in the figure as surface one and two respectively. And this is the reason that we have two centers of curvature of a lens.

Radius of Curvature: From the radius of curvature we understand that it is the radius of the circle formed with the curved part of the lens which is formed from the combination of two parts of the sphere that is represented in the figure as surface one and two respectively. We can also say that it is the distance between the optical center and center of curvature.

Note: Remember that the two spheres which we used to find the radius and center of the lens are identical to each other. Also keep in mind that in case of a concave and concave mirror case we have only one center of curvature and one radius of curvature as they are formed by one sphere only.