What happens to the location of the image when the radius of curvature changes?
I think it moves farther away when the curvature increases.
You are correct! When the radius of curvature of a mirror or lens changes, the location of the image also changes. Specifically, when the radius of curvature increases (becomes larger), the image moves farther away from the mirror or lens.
To understand why this happens, let's consider a concave mirror as an example. A concave mirror is a mirror with a curved surface that bulges inward. When an object is placed in front of a concave mirror, light rays from the object reflect off the mirror and form an image.
The distance between the mirror and the image is called the image distance. This distance depends on the radius of curvature of the mirror. The radius of curvature is the distance between the center of the mirror and the surface of the mirror.
When the radius of curvature increases, it means the mirror becomes less curved, or flatter. In this case, the light rays from the object will reflect off the mirror at a shallower angle. Due to this change in reflection angle, the light rays will converge at a point that is farther away from the mirror.
Therefore, the image distance increases as the radius of curvature increases, causing the image to move farther away from the mirror. Conversely, if the radius of curvature decreases, the mirror becomes more curved, resulting in a smaller image distance and the image moving closer to the mirror.
It's important to note that this explanation applies to concave mirrors, while for convex mirrors, the image formed is always virtual, upright, and located closer to the mirror compared to the object's position. In the case of lenses, similar principles apply, but with some differences based on whether the lens is convex or concave.