Chapter 34, Problem 34.1DQ

A spherical mirror is cut in half horizontally. Will an image be formed by the bottom half of the mirror? If so, where will the image be formed?

To determine

The formation of the image by the bottom half of the mirror and its position.

Explanation of Solution

The radius of curvature of the spherical mirror does not change when it is cut horizontally along the optic axis.

For a spherical mirror, the radius of curvature is twice the focal length of the mirror. If the spherical mirror is cut into half in the horizontally along its optic axis, the radius of curvature of the bottom half of the mirror will not change. That means, the radius of the curvature of the bottom half of the mirror will be equal to the twice of its focal length.

Since the radius of curvature and focal length of the mirror is bottom half of the mirror is same as earlier, so the image formation by this mirror will not change. Thus, the bottoms half of the spherical mirror will formed an image identical to the image that formed before it were cut.

Conclusion: Therefore, the bottoms half of the spherical mirror will formed an image identical to the image that formed before it were cut.