Chapter 23, Problem 1Q

To determine

To analyze:

Whether it is reasonable to burn the whole Roman fleet in the harbor of Syracuse, Italy, by focusing the rays of the Sun with a huge spherical mirror

Answer to Problem 1Q

Solution:

No, it is not reasonable to burn the whole Roman fleet in the harbor of Syracuseby focusing the rays of the Sun with a huge spherical mirror.

Explanation of Solution

Archimedes, to initiate the mission planned to focus the Sun rays by the cancave mirror (A spherical mirror).

The ray from SUN (which is at infinity)comes parallel to the principle axis of the concave mirror. The rays after reflection focus at the point called the focal point of the mirror. Hence, the image of the sun is formed at the focal point which produces immense heat that will set ablaze the ship.

This situation is explained using the diagram.

By this set up, one ship at a time can be burnt. The whole of the harbor of Syracuse, Italy cannot be burnt at once,even though a very large spherical mirror with the big center of curvature had been used.

With the help of the above schematic explanation, the following conclusions are made.

It is not reasonable to burn the whole Roman fleet in the harbor of Syracusewith a spherical mirror. It may be possible to start them on fire one at a time. Archimedes could focus the Sun’s rays down to a single point with a spherical mirror, which would get this one point hot enough to burn a ship, but it is not possible to do this over a large area like an entire harbor.

The other problem is that the spherical mirror he had would only have one focal length, so he would have to be the same distance from each ship that he started on fire. If one ship was farther away than another, then he would have to move closer to the harbor to start the farther ship on fire. This would take a long time and he would have to move his mirror over large distances just to burn the ships one at a time. This would also require a very precisely ground and polished mirror that is huge and has an extremely long focal length, which would have been difficult in Archimedes time.