An object of height 3 cm is placed in front of a concave mirror at 10 cm. If the height of the image is also 3 cm, then radius of curvature of the mirror is

The problem can be solved using the mirror formula and the magnification formula in optics.

The mirror formula is 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.

The magnification formula is -v/u = h'/h, where h' is the height of the image and h is the height of the object.

Given in the problem, the object height h = 3 cm, the image height h' = -3 cm (the negative sign indicates that the image is inverted), and the object distance u = -10 cm (the negative sign indicates that the object is on the same side as the light source).

Substituting these values into the magnification formula gives -v/(-10) = -3/3, which simplifies to v = 10 cm.

Substituting v = 10 cm and u = -10 cm into the mirror formula gives 1/f = 1/10 + 1/(-10), which simplifies to 1/f = 0, so f = infinity.

The radius of curvature R of the mirror is twice the focal length, so R = 2f = 2*infinity = infinity.

Therefore, the radius of curvature of the mirror is infinity, which means the mirror is a plane mirror.