Spherical wavefronts of radiation emanate from point sources of light. As the electromagnetic wavefront expands, it carries energy and momentum that become more dispersed as the wavefront gets larger. If the distance between a light source and detector ( such as the human eye ) is infinite, the light detector will intercept a small component of the spherical wavefront that is essentially flat. As a consequence, thin convex lenses have a maximum capacity to focus electromagnetic wavefronts when they arrive from infinity; however, a thin convex lens’s capacity to focus light rays diminishes when a light source approaches it. If a light source is located at the focal length ( F ) of a thin convex lens, the lens has no capacity to focus the light rays, and the light emerging from the lens is graphically represented as parallel rays that travel into infinity without convergence. For this reason, the simplest approach to studying convex lens ray-diagrams begins with placing a light source an infinite distance from the lens. Subsequently, geometrical analyses of a convex lens’s decreasing ability to focus light rays as light source’s approach can be made.
The primary ray of interest in thin convex lens diagrams is the ray that passes through the center of the lens from an angle. When a light ray passes through the center of a thin convex lens from an angle, it will not be bent or deflected by the lens; nonetheless, as a light source gets closer to the lens, the ray that passes through the lens’s center will do so at increasingly sharper angles relative to the horizontal axis. Conversely, the component of a wavefront that passes through the lens perpendicularly will be refracted inward by the lens. This accompanying ray is used to determine the height of an image ( if any ) that is formed when ( or if ) the pair of rays converge on the opposite side of the lens; however, the location of the image behind the lens is a function of the ray that passes through the lens’s center. This will be the case up to the point that the light source is positioned at the focal length of the lens. When an approaching light source passes the focal length, the energetics of the emerging wavefront will differ, and the light detector will interpret the image in a distorted “ virtual “ manner.
When an essentially flat “ plane “ of electromagnetic radiation travelling from infinity passes through a thin convex lens at an angle, the pair of rays that represent the wave will converge on the opposite side of the lens as an inverted ( vs. upright ) image. Images that form when rays converge and intersect on the opposite side of the lens are defined as being real images. When parallel rays arrive from infinity, the height of the inverted image will be diminished. Furthermore, the inverted image is located at the focal point on the opposite side of the lens. By symmetry, when a light source is located at the focal point in front of the lens, the light rays emerge parallel to one another and travel indefinitely without convergence; thus, a light detector located behind the lens at infinity will observe the image as being upright, virtual, and magnified.
The first symmetry in height between the light source and the image it produces is observed when the source is in front of the lens at a distance that is twice the focal length ( 2F ). The image produced has a height equal to the height of the light source, it is real and inverted, and it is located a distance of ( 2F ) behind the lens. The only ambiguity that remains regards the location, magnification ( if any ), and orientation of images formed when a light source is located further than ( 2F ) in front of a thin convex lens, when it is located between ( 2F ) and ( F ), and when the light source passes ( F ) and is positioned immediately in front of the lens.
When a light source is positioned a distance > ( 2F ), the angle between the wavefront that passes through the center of the lens ( relative to the horizontal axis ) is less than what it would be if the light source were closer to the lens. Recall that symmetry between source and image distance and height existed when the source was located at ( 2F ). Since the light source is now farther than ( 2F ) from the lens, the image formed will still be inverted and real, but it will be diminished and positioned between ( F ) and ( 2F ) behind the lens. Conversely, when the light source is located between ( 2F ) and ( F ) in front of the lens, the image produced will once again be inverted and real, but it will now be magnified and located at a distance greater than ( 2F ) behind the lens.
Finally, the lens will no longer have the capacity to make light rays converge or emerge parallel to one another when a light source passes ( F ) and is directly in front of a thin convex lens. At this location, the pair of light rays will diverge as they leave the lens; thus, a real image cannot be created behind the lens. Instead, an illusory perception is interpreted by the light detector. This virtual illusion is interpreted as being upright and magnified, and it is interpreted by the light detector as being in front of the lens.
RENAISSANCE PHYSICS 