Generally, when dealing with lenses, the mirror equation is renamed the Lens Equation. I derived delta myself and arrived at the same formula you gave so I assume it's correct, but I can't figure out why adding delta to BFD doesn't yield the formula for EFL that I have found in numerous sources. Diffractive optical elements can function as lenses. An object 5 cm high is held 25 cm away from a converging lens of focal length 20 cm. Both the mirror equation and the magnification equation apply to lenses.  The reciprocal of the focal length, 1/f, is the optical power of the lens. Other kinds of aberration include field curvature, barrel and pincushion distortion, and astigmatism. The linear magnification of an imaging system using a single lens is given by. A Fresnel lens has its optical surface broken up into narrow rings, allowing the lens to be much thinner and lighter than conventional lenses. They are used to focus light into a line, or to convert the elliptical light from a laser diode into a round beam. These were formerly complex to make and often extremely expensive, but advances in technology have greatly reduced the manufacturing cost for such lenses.  This was the start of the optical industry of grinding and polishing lenses for spectacles, first in Venice and Florence in the late 13th century, and later in the spectacle-making centres in both the Netherlands and Germany. The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave. A diffraction-limited lens is one in which aberrations have been reduced to the point where the image quality is primarily limited by diffraction under the design conditions. Chromatic aberration. Move the point named " Focus' " to the right side of the lens to change to a concave lens. The focal length of a lens in air can be calculated from the lensmaker's equation:. Lenses are classified by the curvature of the two optical surfaces. Linear magnification M is not always the most useful measure of magnifying power. Careful design of the lens system for a particular application minimizes the aberration. where M is the magnification factor defined as the ratio of the size of an image compared to the size of the object. Consequently, for external lens surfaces as diagrammed above, R1 > 0 and R2 < 0 indicate convex surfaces (used to converge light in a positive lens), while R1 < 0 and R2 > 0 indicate concave surfaces. Lens maker’s formula for a double concave lens. For instance, using a magnifying glass of 5 cm focal length, held 20 cm from the eye and 5 cm from the object, produces a virtual image at infinity of infinite linear size: M = ∞. Typically the lens axis passes through the physical centre of the lens, because of the way they are manufactured. Convex lenses produce an image of an object at infinity at their focus; if the sun is imaged, much of the visible and infrared light incident on the lens is concentrated into the small image. x The word lens comes from lēns , the Latin name of the lentil, because a double-convex lens is lentil-shaped. The sign convention here dictates that if M is negative, as it is for real images, the image is upside-down with respect to the object. If d is small compared to R1 and R2, then the thin lens approximation can be made. In many cases these aberrations can be compensated for to a great extent by using a combination of simple lenses with complementary aberrations. If the lens is biconcave or plano-concave, a collimated beam of light passing through the lens is diverged (spread); the lens is thus called a negative or diverging lens. Move the point named " Focus' " to change the focal length. Spherical aberration A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (elements), usually arranged along a common axis. What is the radius of curvature required if the focal length is to be 20 cm? The lens formula is applicable both in convex lenses and concave lenses. − Using an inappropriate measurement of magnification can be formally correct but yield a meaningless number. Since the diverging light rays emanating from the lens never come into focus, and those rays are not physically present at the point where they appear to form an image, this is called a virtual image. The plane perpendicular to the lens axis situated at a distance f from the lens is called the focal plane. = Lenses can become scratched and abraded. A large lens creates enough intensity to burn a flammable object at the focal point.