A paperweight ( = 1.5 ) shaped as a hemisphere of radius 3.0 cm is placed to hold down a printed page. An observer views the page vertically through the paperweight. At what height above the page will the printed letters near the centre appear to the observer?

Step-by-step solution

For refraction at a spherical surface, the formula is: ₂ v - ₁ u = ₂ - ₁ R Here, light travels from the glass paperweight to the air. Therefore, the refractive index of the first medium is ₁ = 1.5 and the second medium is ₂ = 1.0 . The printed letters are located at the center of the flat surface, which is also the center of curvature of the spherical surface. Taking the pole of the spherical surface as the origin and the downward direction as negative, we have: u = -3.0 cm R = -3.0 cm Substituting these values int