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Focal length

In optics, the focal length of a lens or curved mirror is defined as the distance from its optical center (or principal plane) to the point where incoming parallel rays of light converge (for converging optics) or appear to diverge (for diverging optics) after passing through or reflecting off the device. This distance, typically measured in millimeters or meters, quantifies the lens's or mirror's ability to bend light and is a fundamental property influencing image formation. For thin lenses, the focal length f relates object and image distances via the lens equation \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}, where d_o is the object distance and d_i is the image distance. The value of the focal length depends on the lens's material properties, such as the index of of the , the of its surfaces, and the surrounding medium (usually air). Converging () lenses have a positive focal length, focusing to a real , while diverging () lenses have a negative focal length, producing a virtual . In mirrors, a surface converges with a positive focal length equal to half the , whereas a mirror diverges with a negative value. Shorter focal lengths correspond to stronger bending, enabling wider fields of view, while longer ones provide narrower views with greater . Focal length plays a critical role in optical instruments and imaging systems. In and , it determines the angle of view: lenses with focal lengths around 50 mm on full-frame s produce a "" perspective similar to , wide-angle lenses (e.g., 24 mm or less) capture broader scenes, and telephoto lenses (e.g., 200 mm or more) isolate distant subjects with compressed s. For a given sensor size, the effective scales with focal length, influencing and distortion. In telescopes and microscopes, precise focal lengths enable and , with the system's overall performance often derived from the focal lengths of individual components. Effective focal length accounts for thick lenses or lens groups by measuring from principal planes rather than physical centers, ensuring accurate design in complex systems.

Basic Concepts

Definition

The focal length of an optical system, such as a lens or mirror, is defined as the distance from the system's optical center (or principal plane) to its focal point, where a bundle of parallel incident rays converges to a point after refraction or reflection in converging systems, or appears to diverge from a point in diverging systems. Optical systems possess two principal focal points: the anterior focal point on the object side, from which parallel rays diverging toward the would emerge parallel after passing through it, and the posterior focal point on the image side, where parallel rays incident on the converge (for real images) or from which they appear to diverge (for virtual images). The focal length is conventionally the from the optical center to the posterior focal point, determining the 's focusing power. The term and concept originated in the 17th century, with introducing the idea of the in his 1637 treatise La Dioptrique, describing it as the convergence point of parallel rays refracted by a or surface. later formalized aspects of focal length through experimental investigations of light and in his 1704 work . Focal lengths are positive for converging elements like lenses and concave mirrors, which bring parallel rays to a real on the opposite side of the incident light, and negative for diverging elements like lenses and mirrors, which create a on the incident side. For example, a with a 50 mm focal length converges sunlight to ignite tinder at its posterior , while a with a -20 mm focal length causes parallel rays to diverge as if originating from an anterior point. Basic ray diagrams illustrate this for parallel incident rays along the optical axis. For a converging lens, rays pass through the lens and intersect at the posterior focal point F:
  • A ray through the optical center passes undeviated.
  • A ray parallel to the axis refracts through F.
  • The rays converge at F, a distance f (positive) from the lens.
For a diverging lens, rays diverge after passing through, appearing to originate from the anterior focal point F:
  • The central ray passes undeviated.
  • The parallel ray refracts away from the axis, back-traced to F.
  • The virtual focus is at f (negative) on the incident side.

Sign Conventions

In optics, sign conventions provide standardized rules for assigning positive or negative values to distances and focal lengths in calculations, ensuring consistency and accuracy across different optical systems. The most widely adopted is the Cartesian sign convention, which assumes light propagates from left to right along the . Under this convention, distances measured to the left of the reference point (such as the ) are negative, while those to the right are positive; object distances are thus typically negative for real objects on the incident side, image distances are positive for real images on the transmitted side and negative for virtual images on the incident side, and heights above the are positive while those below are negative. For focal length specifically, the Cartesian convention assigns a positive value to converging lenses or systems that focus rays to a on the transmitted side, and a negative value to diverging lenses or systems that cause rays to appear to diverge from a point on the incident side. For example, a (converging) lens has a positive focal length (+f), enabling formation for distant objects, whereas a (diverging) lens has a negative focal length (-f), producing only images. This approach aligns with the lensmaker's and , where the sign of f directly influences the predicted image location and nature. An alternative is the Newtonian sign convention, introduced by in his 1704 work , which measures object and image distances from the principal focal points rather than the lens itself, with the equation taking the form x_o x_i = f^2, where distances are positive in the direction of incident light for real objects and images. In this system, object distance x_o is positive when the object lies to the left of the front focal point, and image distance x_i is positive when the image lies to the right of the rear focal point, while f remains positive for converging lenses. Although less common in modern computations, the Newtonian convention simplifies certain ray tracing scenarios by treating distances as inherently positive for typical configurations. Adhering to these conventions is crucial in multi-element optical systems, such as compound lenses or telescopes, where inconsistent signing could lead to erroneous predictions of image position, , or aberration corrections, potentially compromising system performance. The Cartesian convention predominates in contemporary and physics due to its compatibility with vector-based ray tracing and computational software.

Lens Models

Thin Lens Approximation

The thin lens approximation models a lens as having negligible thickness relative to its focal length, such that the principal planes coincide at a single point at the lens center. This assumption simplifies ray tracing by treating the lens as an infinitesimally thin that refracts rays without displacement along the . A lens qualifies as thin when its thickness t is much smaller than the radii of of its surfaces. The equation, also known as the Gaussian lens formula, relates object distance o, image distance i, and focal length f as \frac{1}{o} + \frac{1}{i} = \frac{1}{f}. This equation is derived from of , n_1 \sin \theta_1 = n_2 \sin \theta_2, applied successively at the two lens surfaces, under the paraxial approximation where angles \theta with the are small enough that \sin \theta \approx \tan \theta \approx \theta (in radians). For a entering from air (n_1 = 1) into the lens medium (n_2 = n) at the first surface with radius R_1, the paraxial form yields the refraction angle change; a similar step applies at the second surface with radius R_2. Combining these using geometry of similar triangles for parallel incident rays leads to the focal length definition and the full imaging relation. The lateral magnification m under this model is m = -\frac{i}{o} = \frac{h_i}{h_o}, where h_i and h_o are the and object heights, respectively; the negative sign denotes an inverted image for real (positive i) cases. This follows directly from similar triangles in the ray diagram, where rays through the center remain undeviated. The focal length f for a symmetric biconvex in air is given by the lensmaker's equation: \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right), with n the of the material and R_1, R_2 the radii of curvature (positive if the center lies to the right of the surface, per Cartesian ). This equation emerges from summing the powers of the two refracting surfaces under the limit. While useful for first-order optics, the thin lens approximation has limitations: it neglects the physical thickness of the lens, which shifts principal planes in real systems, and ignores aberrations arising from the paraxial assumption, such as (failure of peripheral rays to focus at the same point) and (wavelength-dependent focal length). These effects become significant for large apertures or non-paraxial rays.

Thick and Compound Lenses

In the thick lens model, the focal length is defined with respect to the planes, which are imaginary surfaces where the can be considered to occur for paraxial rays; these planes do not necessarily coincide with the physical center of the lens due to its finite thickness./02%3A_Lens_and_Mirror_Calculations/2.11%3A_Thick_Lenses) The positions of the principal planes depend on the lens's , surface curvatures, and thickness, shifting the effective optical behavior away from the approximation./02%3A_Lens_and_Mirror_Calculations/2.11%3A_Thick_Lenses) The general lensmaker's formula for a thick lens in air accounts for the thickness d and is given by \frac{1}{f} = (n-1)\left(\frac{1}{R_1} - \frac{1}{R_2} + \frac{(n-1)d}{n R_1 R_2}\right), where f is the effective focal length, n is the of the material, and R_1 and R_2 are the radii of of the first and second surfaces, respectively (with sign conventions based on the surface's relative to the light direction)./24%3A_Geometric_Optics/24.3%3A_Lenses) This equation extends the thin lens case by incorporating the term involving d, which becomes negligible when the thickness is small compared to the radii./24%3A_Geometric_Optics/24.3%3A_Lenses) For compound lens systems, composed of multiple elements, the effective focal length (EFL) describes the overall focusing power as if it were a single . When thin lenses are in contact, the reciprocal of the EFL is the sum of the reciprocals of the individual focal lengths: \frac{1}{\text{EFL}} = \sum \frac{1}{f_i}. In such systems, the back focal length (BFL) is the distance from the last lens surface to the rear , while the front focal length (FFL) is the distance from the first lens surface to the front ; these lengths differ from the EFL and are critical for mounting the system with image sensors or objects. A more general approach for multi-element systems, including separations between lenses, uses (also known as ABCD matrix method), where the overall matrix for the system is the product of individual matrices for at surfaces, through media, and translations. The EFL is then derived from the matrix element C as \text{EFL} = -1/C for paraxial rays entering parallel to the . This method efficiently computes the EFL, principal plane locations, and other parameters without explicit ray tracing for complex arrangements. In practical examples, zoom lenses achieve variable EFL by mechanically adjusting the relative positions of lens elements, allowing the effective focal length to range continuously, such as from 24 mm to 70 mm in a standard photographic zoom, to alter without changing lenses. Anamorphic lenses, used in , exhibit different horizontal and vertical focal lengths due to cylindrical elements that squeeze the image asymmetrically, resulting in, for instance, a horizontal EFL half that of the vertical for a 2x squeeze factor, enabling formats with distinctive effects.

Applications in Imaging

Photography

In photography, focal length plays a crucial role in determining the characteristics of an image captured by a lens on a camera sensor or film. Lenses are classified based on their focal length relative to the 35mm full-frame format, which serves as a standard reference. Wide-angle lenses have focal lengths shorter than 35mm, providing expansive views suitable for landscapes and architecture; normal lenses approximate 50mm, offering a field of view similar to the human eye for natural-looking portraits and street photography; and telephoto lenses exceed 70mm, enabling magnification of distant subjects like wildlife or sports without physical approach. The primary effect of focal length is on the angle of view, which defines how much of the is captured. For a given size, shorter focal lengths yield wider angles, while longer ones produce narrower fields. This relationship is approximated by the formula \theta \approx 2 \arctan\left(\frac{s}{2f}\right), where \theta is the angle of view, s is the dimension (e.g., width or ), and f is the focal length; thus, increasing f narrows \theta, compressing the visible into a tighter . Focal length also influences perceived , though the distortion arises primarily from camera-to-subject rather than the itself. To maintain consistent subject framing with a shorter focal length (e.g., wide-angle), photographers must position closer to the subject, exaggerating foreground elements and creating a of depth or in features like facial proportions. Conversely, longer focal lengths (e.g., telephoto) allow greater for the same framing, compressing the scene and flattening the apparent separation between foreground and background, which is often used for flattering portraits or isolating details. Focal length interacts with and subject distance to affect (DOF), the range of distances appearing acceptably sharp. Longer focal lengths generally reduce DOF for a given and distance, isolating subjects against blurred backgrounds—a technique prized in portraiture. An approximate formula for DOF when the subject distance g \gg f is \text{DOF} \approx \frac{2 N c g^2}{f^2}, where N is the (), c is the circle of confusion (a measure of acceptable blur), and g is the subject distance; this highlights how larger f shallows DOF. On cameras with smaller sensors, such as or Micro Four Thirds, the adjusts the effective focal length to equate to full-frame equivalents. The is the ratio of the full-frame sensor diagonal (43.3mm) to the smaller sensor's diagonal; for example, a 1.5× (common in ) multiplies the lens focal length by 1.5, so a 50mm lens behaves like a 75mm on full-frame, narrowing the angle of view without altering the physical lens properties. The standardization of focal lengths like 50mm traces to early 20th-century innovations, particularly the Leica I camera introduced in 1925, which popularized the 35mm film format with a 50mm lens as the default, establishing it as the "normal" view that mimicked human vision and influencing lens design across the industry.

Telescopes and Microscopes

In telescopes, the focal length plays a crucial role in determining angular magnification and light-gathering capability. For a basic refracting telescope, the angular magnification M is given by M = -\frac{f_\text{objective}}{f_\text{eyepiece}}, where f_\text{objective} is the focal length of the objective lens and f_\text{eyepiece} is that of the eyepiece, producing an inverted image. The light-gathering power, which enables detection of faint objects, is primarily set by the objective's aperture diameter D, with collecting area proportional to D^2; the focal ratio f/D influences the system's "speed," where lower ratios concentrate light more efficiently for brighter images. The resolution of telescopes is fundamentally limited by diffraction, with the angular resolution \theta \approx 1.22 \lambda / D, where \lambda is the wavelength of light; this limit is independent of focal length, but the f/D ratio affects the linear resolution at the focal plane, as the image scale is proportional to f. For example, the Hubble Space Telescope features a 2.4-meter primary mirror with an effective focal ratio of f/24, enabling high-resolution imaging across ultraviolet to near-infrared wavelengths despite its diffraction-limited performance. In microscopes, focal lengths determine the total magnification and working distance in compound systems. The total magnification M is the product of the objective magnification m_\text{objective} and eyepiece magnification m_\text{eyepiece}, where m_\text{objective} = L / f_\text{objective} and L is the standard tube length (typically 160–200 mm); shorter objective focal lengths yield higher but reduce the working distance, the gap between the front lens and specimen. Microscopes operate as finite conjugate systems, forming real images at intermediate planes for further , in contrast to the afocal (infinite conjugate) design of telescopes, where parallel input rays produce parallel output rays without intermediate focusing. Resolution in microscopes is also diffraction-limited, influenced by the objective's (related to D / (2f)), but the short focal lengths enable high f/D ratios for detailed imaging. For instance, oil immersion objectives, used for 100× , typically have focal lengths around 2 mm to achieve sub-micron when immersed in oil of matching .

Related Properties

Optical Power

Optical power, denoted as P, quantifies the of an element to converge or diverge light rays and is defined as the reciprocal of its f, expressed in diopters (D), where $1 D = 1 m^{-1}. For lenses operating in air, P = 1/f, with positive values indicating converging (positive) lenses and negative values for diverging (negative) lenses. A lens with a focal length of 1 m thus has a power of +1 D, while a +2 D lens corresponds to a focal length of 0.5 m, commonly used in corrective to focus light onto the . For spherical mirrors, the power follows a similar reciprocal relationship but accounts for , given by P = 2n / R, where R is the and n is the of the incident medium (typically n = 1 in air, yielding P = 2 / R). The sign adjusts for (positive power, converging) or (negative power, diverging) mirrors, emphasizing the role of surface in determining focusing strength. The power of a single spherical refracting surface, separating media with refractive indices n_1 (incident) and n_2 (refracted), is P = (n_2 - n_1) / R, where R is the . This underpins the of more complex elements, such as lenses formed by multiple surfaces, by summing individual surface powers under the thin lens approximation. When combining multiple thin lenses, the total power simplifies based on their configuration. For lenses in contact, the combined power is the algebraic sum of individual powers: P_\text{total} = P_1 + P_2 + \cdots + P_n. If the lenses are separated by a distance d (in meters), the total power becomes P_\text{total} = P_1 + P_2 - d P_1 P_2, accounting for the interaction between the intermediate image formed by the first lens and the second. These relations facilitate the design of compound optical systems by treating power additively while adjusting for spatial separation. In ophthalmic applications, spectacle refers to the prescribed strength measured at a standard (typically 12 mm from the ), but the effective at the eye—known as vertex —requires adjustment for variations in this . For high- prescriptions (e.g., beyond ±4 D), shifting the closer to the eye (as in lenses) reduces the effective converging of positive lenses or increases diverging of negative ones, necessitating recalibration using formulas like the vertex compensation to ensure accurate correction. The concept of optical power as a standardized measure was formalized in the through advancements in paraxial , particularly in Carl Friedrich Gauss's Dioptrische Untersuchungen (), which established systematic methods for calculating powers and combinations in optical instruments.

Field of View

The (FOV) in an optical system refers to the angular extent of the observable scene, which is inversely related to the focal length of the ; shorter focal lengths produce wider FOVs, while longer ones yield narrower views. This relationship allows photographers and optical designers to select lenses that capture the desired spatial coverage, from expansive landscapes to focused details. For lenses, which project straight lines without , the horizontal or vertical FOV \theta is calculated using the \tan(\theta/2) = (d/2)/f, where d is the corresponding dimension (e.g., width or height) and f is the focal length. This equation derives from the of the lens projecting the scene onto the , ensuring a linear . In full-frame cameras with a sensor (24 mm height × 36 mm width), the diagonal FOV is approximately $2 \arctan(43.3 / (2f)), where 43.3 mm is the sensor diagonal and f is in millimeters; this provides a standard reference for comparing coverage. Specialized lenses exhibit extreme FOVs with associated : fisheye lenses, typically with focal lengths under 10 mm (e.g., 6 mm designs), achieve fields exceeding 180° but introduce radial barrel distortion to accommodate the curvature. Conversely, telephoto lenses with focal lengths over 200 mm produce narrow FOVs under 10° (e.g., ~6° at 400 mm), often showing distortion where straight lines bow inward. In non-imaging optical devices like , the FOV, expressed in degrees, is constrained by the focal length of the objective lens and the design; the objective collects light over a wide , while the determines the apparent angular field, typically limiting real FOV to 5–8° for standard 7×50 models. To compare FOV across different sensor formats, the 35 mm equivalence scales the effective focal length by the (e.g., a 50 mm lens on an sensor with 1.5× yields ~75 mm equivalent), standardizing the angular coverage to that of a full-frame system. At extreme FOVs, limitations arise including vignetting, where image brightness falls off at the edges due to cosine-fourth falloff and mechanical obstructions, and geometric distortions like barrel (outward bowing in wide-angle lenses) or (inward in telephotos), which degrade rectilinearity.

References

  1. [1]
    Focal Length of a Lens - HyperPhysics
    The principal focal length of a lens is determined by the index of refraction of the glass, the radii of curvature of the surfaces, and the medium in which the ...
  2. [2]
    Lenses/Optics - Rutgers Physics
    Besides its physical size, the focal length defines the critical property of a lens or mirror. We will discuss the importance of the focal length a bit ...
  3. [3]
    [PDF] Chapter 2 LENSES - cs.wisc.edu
    A strong. lens is one that deflects light a lot, meaning it has a short focal length. The focal length of. camera lenses is always given in millimeters.
  4. [4]
    Lenses and Geometrical Optics - Exploring the Science of Light
    Focal length is the distance from a lens to its focal point. Lenses can be convex (positive focal length) or concave (negative focal length). Convex lenses ...
  5. [5]
    Focal lengths and focal points
    A converging lens focuses light to a focal point. A concave lens's focal length is negative, and its image is always virtual.Missing: definition | Show results with:definition<|control11|><|separator|>
  6. [6]
    [PDF] Lecture 18: - CS184/284A Homepage
    Examples of focal lengths on 35mm format: • 17mm is wide angle 104°. • 50mm is a “normal” lens 47°. • 200mm is telephoto lens 12°. • Careful!
  7. [7]
    [PDF] lenses and apertures - Stanford Computer Graphics Laboratory
    Apr 13, 2010 · Does sensor size affect DoF? ! as sensor shrinks, lens focal length f typically shrinks to maintain a comparable field of view.
  8. [8]
    [PDF] Methods for measuring a lens focal length
    • By definition, the effective focal length EFL is the distance between the rear principal point P', and the rear focal point F' of the lens. •
  9. [9]
    Focal Length - StatPearls - NCBI Bookshelf
    Nov 14, 2023 · Focal length is the distance between the lens and the focal point, where the light rays converge or diverge.
  10. [10]
    Optics and Refraction | Ento Key
    Nov 20, 2022 · ... posterior focal point in the normal eye. The optic axis passing ... Anterior focal point (F 1) (anterior focal distance). –15.7 mm in ...
  11. [11]
    The Project Gutenberg eBook of Opticks:, by Sir Isaac Newton, Knt.
    The Lens which I used in the second and eighth Experiments, being placed six Feet and an Inch distant from any Object, collected the Species of that Object by ...
  12. [12]
    2.4 Thin Lenses - University Physics Volume 3 | OpenStax
    Sep 29, 2016 · The distance from the center of the lens to its focal point is the focal length f of the lens. Figure a shows rays parallel to the optical axis ...
  13. [13]
    Thin-Lens Equation:Cartesian Convention - HyperPhysics
    Cartesian Sign Convention​​ The refractive power of a surface that makes light rays more convergent is positive. The focal length of such a surface is positive.
  14. [14]
    [PDF] 5.2 Lenses - Oregon State University
    This is the Newtonian form of the lens equation, the first state- ment of which appeared in Newton's Opticks in 1704. The signs of and x are reckoned with ...
  15. [15]
    Thin Lenses – University Physics Volume 3 - UCF Pressbooks
    The distance from the center of a thin lens to its focal point is called the focal length f. Ray tracing is a geometric technique to determine the paths ...
  16. [16]
    [PDF] Chapter 10 Image Formation in the Ray Model
    Snell's Law in the Paraxial Approximation. Recall Snell's law that relates the ray angles before and after refraction: n1 sin [θ1] = n2 sin [θ2]. In the ...
  17. [17]
    [PDF] Section 4 Imaging and Paraxial Optics
    This is the Paraxial Refraction Equation. The two derivations of the paraxial raytrace equation produce the same results, but the traditional derivation ...
  18. [18]
    [PDF] THIN LENSES - Web Physics
    THIN LENSES. OBJECTIVE. To verify the thin lens equation, f d d i o. 1. 1. 1. = +. , and the magnification equations m = hi/ho = –di/do. THEORY. In the above ...
  19. [19]
    Lens-Maker's Formula and Thin Lenses - HyperPhysics
    For a thin lens, the power is approximately the sum of the surface powers. ... For thick lenses , Gullstrand's equation can be used to calculate the lens power.Missing: derivation | Show results with:derivation
  20. [20]
    [PDF] Lecture 27 - Purdue Physics department
    • Even the thick lens equation makes approximations and assumptions. – Spherical lens surfaces. – Paraxial approximation. – Alignment with optical axis. • The ...
  21. [21]
    Principal Planes for Lenses - HyperPhysics
    To use the lens equation for the thick lens, we must find the object distance to the first principal plane H1, so we must calculate the distance from the ...
  22. [22]
    Lensmaker's Equation - StatPearls - NCBI Bookshelf
    Jul 8, 2023 · Equation 1. Lensmaker Equation. 1/f = (n-1) ⋅ [(1/R1) – (1/R2) + {[(n-1)d]/(n⋅R1⋅R2)}], where. f: Lens focal length. n: Lens material refractive ...
  23. [23]
    https://www.edmundoptics.com/knowledge-center/application-notes/optics/understanding-optical-lens-geometries/
  24. [24]
    Focal Length – focal distance, dioptric power, curved mirror, lens ...
    The front focal distance is thus the distance between front focal point and the entrance surface of the optics, while the back focal distance is the distance ...
  25. [25]
    ABCD Matrix – ray transfer matrix - RP Photonics
    An ABCD matrix [1] is a 2-by-2 matrix associated with an optical element which can be used for describing the element's effect on a laser beam.What Are ABCD Matrices? · Ray Optics · ABCD Matrices of Important...
  26. [26]
    [PDF] Lecture Notes on Geometrical Optics (02/18/14)
    The composite lens does not have the same apparent focusing length in front and back end! c) d=f1+f2: parallel beams illuminating the composite lens will remain ...
  27. [27]
    [PDF] A STUDY ON ZOOM LENSES - The University of Arizona
    First, there is the variator or zooming group. This is made up of one or more groups of lenses that provide the focal length change to vary the magnification of ...<|control11|><|separator|>
  28. [28]
    Understanding Focal Length and Field of View
    ### Extracted Formula and Summary
  29. [29]
    Understanding Anamorphic Lenses - RED cameras
    Anamorphic lenses compress images along the longer dimension, requiring stretching. They were originally for wide format film, and now give a unique look with ...
  30. [30]
    Something You Need to Know About Anamorphic Lenses - DZOFILM
    The inconsistency between the vertical focal length and the horizontal focal length causes its unique "waterfall out-of-focus". It cannot be equivalently ...
  31. [31]
    Understanding focal length in photography - Canon Georgia
    Wide-angle lenses – loosely defined as lenses with a wider field of view than the human eye – are lenses with a focal length up to around 35mm. · Standard lenses ...
  32. [32]
    Introduction to Visual Literacy: Digital Images and Photography
    Apr 11, 2025 · Wide-angle lenses are considered to be 35mm and below; "normal" lenses are around 40mm to 60mm, short telephoto around 85mm to 135mm and long ...Missing: classifications reliable
  33. [33]
    Does Focal Length Distort Subjects? - Photography Life
    Oct 28, 2020 · Focal length affects how tight our subjects appear in the frame, but it does absolutely nothing to affect the perspective.
  34. [34]
    Understanding Depth of Field in Photography - Cambridge in Colour
    Depth of field refers to the range of distance that appears acceptably sharp. It varies depending on camera type, aperture and focusing distance.
  35. [35]
    Understanding Depth of Field - A Beginner's Guide - Photography Life
    Oct 10, 2024 · For a given size of the subject's image in the focal plane, the same f‑number on any focal length lens will give the same depth of field. This ...What is Depth of Field? · Camera-Subject Distance · Focal Length of the Lens
  36. [36]
    Understanding Crop Factor | B&H eXplora
    Jul 27, 2015 · A 50mm lens on a camera with a 1.5x crop factor APS-C sensor gives a field of view equivalent to that of a 75mm lens on a full-frame or 35mm ...
  37. [37]
    One Hundred Years of Leica: How a Tiny German Camera Changed ...
    Aug 1, 2025 · The 50mm focal length remains a gold standard, with possibly more 50mm lenses produced than any other focal length. The idea of a compact, go- ...
  38. [38]
    [PDF] Calculating the Magnification of a Telescope - Space Math @ NASA
    For example, if the telescope objective has a focal length of 2000 millimeters and the eyepiece has a focal length of 4 millimeters, H/h = 2000/4 = 500, so the ...
  39. [39]
    Unit 15 Answers 03 C
    The angular magnification of the telescope is m = fo / fe. The length of the telescope barrel is (fo +fe), since fe is very nearly equal to the object distance ...
  40. [40]
    [PDF] Optics and Telescopes - NJIT
    McMath-Piece Telescope has 1.52 m aperture, and f ratio of 56.58. ... Light Gathering Power. ❑ Aperture diameter D: effective diameter of the telescope.
  41. [41]
    [PDF] Telescopes and Detectors - Astronomy in Hawaii
    The smaller the f-ratio, the “faster” the telescope (i.e. it concentrates more light in a small area). 2.2 Magnification. The main purpose of a telescope is to ...<|separator|>
  42. [42]
    Super-resolution optical telescopes with local light diffraction ...
    Dec 18, 2015 · Suffering from the diffraction of light, the resolution of a telescope is theoretically limited by the diameter D of the objective aperture and ...
  43. [43]
    [PDF] 6.2 Interference and diffraction - Physics Courses
    The diffraction limit limits the smallest objects that can be resolved by an optical system. A camera has an f/1.4 lens, meaning the ratio of focal length to ...
  44. [44]
    [PDF] The Hubble Space Telescope (HST) has - NASA
    The secondary mirror has a magnification of. 10.4X, converting the primary-mirror converging rays from f/2.35 to a focal ratio system prime focus of f/24 and ...
  45. [45]
    Microscope - HyperPhysics Concepts
    Linear magnification of objective = mo = Angular magnification of eyepiece = Me = Total magnification = M = The tube length and the objective and eyepiece focal ...
  46. [46]
    26.4 Microscopes – College Physics - UCF Pressbooks
    The overall magnification of a multiple-element system is the product of the individual magnifications of its elements. Microscope Magnification. Calculate the ...
  47. [47]
    Microscopes – Introductory Physics for the Health and Life Sciences II
    The focal length of an objective lens is different than the working distance. This is because objective lenses are made of a combination of lenses and the focal ...
  48. [48]
    [PDF] Section 14 Relays and Microscopes
    In many systems, the relay works at approximately 1:1 conjugates or magnification. The object distance for the relay lens is then twice the focal length of the ...
  49. [49]
    [PDF] Section 15 Telecentric Systems
    An afocal system is made double telecentric by placing the system stop at the common focal point. The chief ray is parallel to the axis in object space and ...Missing: instruments | Show results with:instruments
  50. [50]
    Basic Principles of Infinity Optical Systems - Zeiss Campus
    The objective magnification (M) is calculated by dividing the reference focal length (L) of the tube lens by the objective focal length (F).Missing: total | Show results with:total
  51. [51]
    Anatomy of the Microscope - Objectives - Molecular Expressions
    Sep 20, 2018 · Working Distance - This is the distance between the objective front lens and the top of the cover glass when the specimen is in focus. In most ...Missing: relation | Show results with:relation
  52. [52]
    Optical Power - RP Photonics
    Quantitatively, the focusing power is the reciprocal of the focal length of the device, and its units are inverse meters (m−1), also called diopters (dpt). The ...
  53. [53]
    Diopter: Measuring Optical Power - Lasikwelt
    Aug 16, 2025 · A diopter is the reciprocal of a lens's focal length in meters. A 1-meter focal length is 1 diopter; 0.5 meters is 2 diopters.
  54. [54]
    Theory of Vergences - UQ Physics
    Vergences for Mirrors ... where Vf= ± n/v is the final vergence, Vi = ± n/u is the initial vergence and P = ± 2n/r is the power of the mirror. Powers also have ...
  55. [55]
    Refractive Power - an overview | ScienceDirect Topics
    Refractive power is defined as the measure of a surface's ability to bend light, quantified in diopters (D), and is calculated using the formula P = (n' ...
  56. [56]
    Surface Power for a Lens - HyperPhysics
    For a thin lens, the power of the lens is approximately the sum of the surface powers. The relationship for lens power is called the lensmaker's formula.Missing: source | Show results with:source
  57. [57]
    Thin Lenses and their Combinations - Formulas | Solved Problems
    Dec 19, 2022 · Problem (IIT JEE 1997): Two thin lenses, when in contact, produce a combination of power +10D + 10 D . When they are 0.25 m apart, the power ...
  58. [58]
    [PDF] Vertex Distance, Effective Power, and Compensated Power – Tilt
    Vertex distance is the distance from the back of a lens to the cornea's apex. It affects lens effective power, and moving a plus lens closer decreases its  ...
  59. [59]
    Effective and Compensated Power - Vertex Difference Calculator
    Calculate how prescription power changes with lens distance using our precise Vertex Difference Calculator.
  60. [60]
    [PDF] Marc Levoy CS 178, Spring 2012
    Focal length and field of view. 31. (London). FOV measured diagonally on a. 35mm full-frame camera (24 ! 36mm). Page 32 ! Marc Levoy. Focal length and field of ...
  61. [61]
    [PDF] Computer Vision
    Aug 31, 2007 · sensor, this would require a lens with a focal length that equation (6) shows to be f = h. 2 tanφ0/2. = 16. 2 tan 0.7 × π/180. ≈ 655 mm, a very ...
  62. [62]
    CS184/284A: Lecture Slides
    If a lens has 180-degree FoV, it has to be a fisheye lens. Some fisheye lenses feature a really wide FoV. For example, Nikon's 6 mm circular fisheye lens ...
  63. [63]
    [PDF] LAB 8: BINOCULARS
    Binoculars are specified by stating their “magnification x diameter of the objective lens”. For example, binoculars with the specification 6 x 30 (read “6 by 30 ...
  64. [64]
    [PDF] Section 23 Camera Systems
    A lens with a focal length equal to the diagonal of the format is usually considered standard.
  65. [65]
    [PDF] 1 optical system design and distortion control of wide field of view ...
    An optical system with constant focal length with this definition will result in a rectilinear image; that is straight lines in the object map to straight ...Missing: formula | Show results with:formula