Final answer:
An image will be located at the focal point of a spherical lens or mirror when the object is at infinity, meaning that the incoming light rays are parallel and will converge at the focal point after being focused by the lens or reflected by the mirror.
Step-by-step explanation:
Under certain circumstances, an image can be located at the focal point of a spherical lens or mirror. For a lens, images are formed at the focal point when parallel rays of light enter the lens and are bent or refracted to meet at the focal point. Conversely, in the case of a mirror, when rays parallel to the principal axis reflect off the surface, they converge at the focal point. This is a basic principle of optics that is critical in the design and function of many optical devices, such as telescopes and cameras.
About the available options, an image will be located at the focal point of a spherical lens or mirror when the object is very far away, effectively at infinity. At such large distances, the rays of light arriving at the lens or mirror are virtually parallel, and by focusing, they converge at the focal point. This is often used in astronomy where telescopes are focused on distant stars and other celestial objects, which are so far away that they appear to be at an 'infinite' distance relative to the focal length of the optical device.
Moreover, the opposite is also true. That is, if rays leave the focal point, after reflection or refraction, they will emerge parallel to the principal axis. This principle is often harnessed in headlight design, where a bulb is placed at the focal point of a parabolic reflector to produce parallel light beams for better illumination at a distance. Therefore, the correct option in this context is when the object is at infinity, which corresponds to option a. This knowledge is valuable for understanding the physics behind lenses and mirrors and their applications in various technologies.