A paperweight ( μ = 1.5 ) in the shape of a hemisphere of radius...

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, $R = 3.0 \text{ cm}$.

When the observer views the letters vertically from above, refraction occurs at the top flat surface. The apparent depth $d'$ of the letters from the top surface is given by:

$d' = \dfrac{R}{\mu}$

Substituting the given values:

$d' = \dfrac{3.0}{1.5} = 2.0 \text{ cm}$

The image of the letters is formed $2.0 \text{ cm}$ below the top flat surface.

Since the top flat surface is at a height of $3.0 \text{ cm}$ from the page, the apparent height of the letters above the page is:

$h = 3.0 \text{ cm} - 2.0 \text{ cm} = 1.0 \text{ cm}$