HiSET Science: Geometric Optics

Real and Virtual Images
In optics, an object's image is what is seen when the object is viewed through a lens. The location of an object's image is related to the lens's focal length by the equation 1/do + 1/di= 1/f, where f is the focal length, and do and di are the distance of the object and its image from the lens, respectively. A positive di indicates that the image is on the opposite side of the lens from the object. If the lens is a magnifying lens, the height of the object may be different from that of its image, and may even be inverted. The object's magnification, m, can be found as m = -di/do. The value for the magnification can then be used to relate the object's height to that of its image: m = yi/yo.
Note that if the magnification is negative, then the image has been inverted.
Images may be either real or virtual. Real images are formed by light rays passing through the image location, while virtual images are only perceived by reverse extrapolating refracted light rays. Diverging lenses cannot create real images, only virtual ones. Real images are always on the opposite side of a converging lens from the object and are always inverted.

Thin Lenses
A lens is an optical device that redirects light to either converge or diverge in specific geometric patterns. Whether the lens converges or diverges is dependent on the lens being convex or concave, respectively. The particular angle of redirection is dictated by the lens's focal length. For a converging lens, this is the distance from the lens that parallel rays entering from the opposite side would intersect. For a diverging lens, it is the distance from the lens that parallel rays entering the lens would intersect if they were reverse extrapolated. However, the focal length of a diverging lens is always considered to be negative. A thin lens is a lens whose focal length is much greater than its thickness. By making this assumption, we can derive many helpful relations.

Concave Mirrors
Concave mirrors will create an image of an object in varying ways depending on the location of the object. The table below details the location, orientation, magnification, and nature of the image. The five object locations to be examined are between the mirror and the focal point (1), at the focal point (2), between the focal point and the center of curvature, or twice the focal point (3), at the center of curvature (4), and beyond the center of curvature (5).




Note in case 5 that the image may effectively be located at the focal point. This is the case for objects at extremely great, or near infinite, distances from the mirror. The magnification at these distances will be very small and a true infinite distance would result in a magnification of zero.

Plane Mirrors and Spherical Mirrors
Plane mirrors have very simple properties. They reflect only virtual images, they have no magnification, and the object's distance from the mirror is always equal to that of its image. Plane mirrors will also appear to reverse the directions left and right.
Spherical mirrors follow the same governing equations for finding image height, location, orientation, and magnification as do thin lenses; however, the sign convention for image location is reversed. A positive image location denotes that it is on the same side as the object. Spherical mirrors may be either concave or convex. Convex mirrors are by far the simpler of the two. They will always reflect virtual, upright images with magnification between zero and one. Concave mirrors have varying behavior based on the object location.

Simple Magnifier, the Microscope, and the Telescope
A simple magnifier, or commonly a magnifying glass, is a converging lens that creates an enlarged virtual image near the observer's eye. The object must be within a certain distance, about 25 cm or 10 inches, from the magnifier for it to operate properly. Otherwise, the image will be blurry.
A microscope is a magnifying device that is used to examine very small objects. It uses a series of lenses to capture light coming from the far side of the sample under examination. Often microscopes will have interchangeable magnification lenses mounted on a wheel, allowing the user to adjust the level of magnification by rotating in a different lens. Optical microscopes will generally be limited to a magnification of 1500.
Telescopes are used to view very distant objects, most often celestial bodies. Telescopes use both lenses and mirrors to capture light from a distant source, focus it, and then magnify it. This creates a virtual image that is very much smaller than the object itself, and yet much larger than the object appears to the naked eye.

Prisms
Prisms are optical devices that alter the path or nature of light waves. Glass and plastic are the two most prevalent materials used to make prisms. There are three different types of prisms in common use. The most familiar of these is the dispersive prism, which splits a beam of light into its constituent wavelengths. For sunlight, this results in the full spectrum of color being displayed. These prisms are generally in the familiar triangular prism shape.
Polarizing prisms, as their name suggests, polarize light, but without significantly reducing the intensity, as a simple filter would. Waves that are oscillating in planes other than the desired plane are caused to rotate, so that they are oscillating in the desired plane. This type of prism is commonly used in cameras.
Reflective prisms are much less common than either of the others. They reflect light, often through the use of the total internal reflection phenomenon. Their primary use is in binoculars.