Question

1. In 214 BC, Archimedes invented a large spherical-type mirror used to focus the sun's intense rays onto far away enemy boats, which would eventually light them on fire. If the boats were travelling in a nearby channel approximately 1,000 m from the river bank, what would the radius of curvature of his mirror need to be? Show your work.

Answer 1

2000 m

Step-by-step explanation:

since the boat is 1000 m from the river bank, the beam must be focused at this point. This indicates that the focal length is 1000 m

for a spherical mirror, the focal length is given by

f = R/2

where R is the radius of curvature

1000 = R/2

R = 2000 m

R = 2000 m

this means that the radius of curvature must be 2000 m