As depicted in the figure, a concave mirror of radius R is placed on a horizontal table. Water (refractive index = ) is poured into the mirror up to a height h . At what position should an object be placed such that its image forms on itself?

Step-by-step solution

For the final image to form on the object itself, the light rays must retrace their path after reflection from the concave mirror. This happens when the rays strike the mirror normally, which means the refracted rays must appear to come from the center of curvature C of the mirror. The center of curvature C is at a distance R from the pole of the mirror. Since the water is filled up to a height h , the distance of C above the water surface is R - h . Let the object be placed at a height x above the water surface. W