# If a concave mirror with a radius of curvature of 0.93 m has an object placed at 0.37 m in front...

## Question:

If a concave mirror with a radius of curvature of 0.93 m has an object placed at 0.37 m in front of it, what is the mirror's focal length? Round your answer to 3 decimal places.

## Concave Mirrors

Spherical concave mirrors are cut from a sphere and therefore, there is a point that is the center of the sphere from which the mirror is cut. We call this point the center of curvature. The distance from the center of curvature to the vertex of the mirror is called the radius of curvature of a mirror, R. The concave mirror also has a focus. The distance from the focus of the mirror to the vertex of the mirror is called the focal length, f.

For spherical mirrors, the following relationship is true:

{eq}R=2*f {/eq}

Assuming this is a spherical concave mirror, we can use the relationship:

{eq}R=2*f {/eq}

Given the radius, R is 0.93 m. Then the focal length can be found:

{eq}R=2*f\\ 0.93 \ m=2*f\\ f=0.465 \ m {/eq}