In the case of a thin lens, how are the centres of curvature typically positioned relative to the optical centre?

Correct option is A

Correct option: (a), They are equidistant from the optical centre.

In the case of a thin lens, the centers of curvature are positioned relative to the optical center as follows:

1. ​Convex lens (biconvex): For a biconvex lens, there are two spherical surfaces—one convex on each side. The centers of curvature of these surfaces are located along the optical axis, on opposite sides of the lens. The center of curvature of the front surface (the surface facing the object) is positioned on the same side as the object, while the center of curvature of the back surface (the surface facing the image) is positioned on the opposite side of the lens. The optical center lies between these two centers of curvature, closer to the front center of curvature.
   
2. Concave lens (biconcave): A biconcave lens also has two spherical surfaces—concave on each side. The centers of curvature for these surfaces are similarly located along the optical axis, but in this case, they are positioned on opposite sides of the lens as well. The center of curvature for the front surface is on the opposite side of the lens from the object, while the center of curvature of the back surface is positioned on the same side as the object. The optical center lies between these two centers of curvature.
   

In both cases, the centers of curvature are located along the optical axis, which is the line connecting the optical center of the lens and the focal points. The distance between the optical center and each center of curvature is equal to the radius of curvature of the corresponding lens surface