A paperweight ( = 1.5 ) in the shape of a hemisphere of radius 3.0 cm is placed to hold down a printed page. The paperweight is inverted in its place such that the spherical surface touches the paper. An observer views the page vertically through the paperweight. Determine the height above the page at which the printed letters near the centre appear to the observer.

Step-by-step solution

The paperweight is inverted, which means its flat surface is horizontal at the top and the spherical surface touches the page at the bottom. For the letters near the center of the page, they are virtually in contact with the pole of the spherical surface. Thus, the real depth of these letters from the top flat surface is equal to the radius of the hemisphere, R = 3.0 cm . When the observer views the letters vertically from above, refraction occurs at the top flat surface. The apparent depth d' of the letters from t