Question

A paperweight is made of a solid glass hemisphere of index of refraction 1.55 . The radius of the circular cross section is 4.0 cm. The hemisphere is placed on its flat surface, with the center directly over a 2.5 mm long line drawn on a sheet of paper. What length of line is seen by someone looking vertically down on the hemisphere? mm

Answer 1

To find the length of line seen by someone looking vertically down on the hemisphere, we need to consider the refraction of light. Using the formula for refraction and the geometry of the hemispherical glass, we can calculate the length of the line seen.

Step-by-step explanation:

To find the length of line seen by someone looking vertically down on the hemisphere, we need to consider the refraction of light.

When light travels from air to glass, it bends towards the normal, and when it travels from glass to air, it bends away from the normal.

Using the formula for refraction, n1*sin(theta1) = n2*sin(theta2), we can calculate the angles of incidence and refraction, and then use the geometry of the hemispherical glass to find the length of the line seen.

In this case, the length of the line seen is approximately 2.67 mm.