A thin concavo-convex glass lens (refractive index 1.5 ) features a convex surface with a 20 cm radius of curvature and a concave surface with a 60 cm radius of curvature. The convex side is silvered and rests on a horizontal surface. A pin is initially positioned on the axis such that its image coincides with it. If the concave section is subsequently filled with water ( = 4/3 ), determine the distance through which

Step-by-step solution

For the image to form at the same location as the object, the light rays must retrace their path. This happens when the rays strike the silvered surface normally, meaning the image formed by the first refraction must lie at the center of curvature of the silvered surface. Let the light travel downwards from the pin. The lens rests on its convex surface, so the bottom surface is convex (bulging downwards) and the top surface is concave (depressed downwards). Applying the sign convention for light coming from above: