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Top: The formation of a real image using a convex lens. Bottom: The formation of a real image using a concave mirror. In both diagrams, f  is the focal point, O  is the object, and I  is the image. Solid blue lines indicate light rays. It can be seen that the image is formed by actual light rays and thus can form a visible image on a screen placed at the position of the image.
An inverted real image of distant house, formed by a convex lens, is viewed directly without being projected onto a screen.
Producing a real image. Each region of the detector or retina indicates the light produced by a corresponding region of the object.

In optics, an image is defined as the collection of focus points of light rays coming from an object. A real image is the collection of focus points actually made by converging/diverging rays, while a virtual image is the collection of focus points made by extensions of diverging or converging rays.[1] In other words, a real image is an image which is located in the plane of convergence for the light rays that originate from a given object. Examples of real images include the image produced on a detector in the rear of a camera, and the image produced on an eyeball retina (the camera and eye focus light through an internal convex lens).[2]

In simple terms, a real point image is formed when all the rays of light from a point object passing through an optical system converge at a single point and a virtual point image is formed when all the rays of light from a point object passing through an optical system seem to come from a single point.[3]

In ray diagrams (such as the images on the right), real rays of light are always represented by full, solid lines; perceived or extrapolated rays of light are represented by dashed lines. A real image occurs at points where rays actually converge, whereas a virtual image occurs at points that rays appear to be diverging from.

Real images can be produced by concave mirrors and converging lenses, only if the object is placed further away from the mirror/lens than the focal point, and this real image is inverted. As the object approaches the focal point the image approaches infinity, and when the object passes the focal point the image becomes virtual and is not inverted (upright image). The distance is not the same as from the object to the lenses.[4]

Real images may also be inspected by a second lens or lens system. This is the mechanism used by telescopes, binoculars and light microscopes. The objective lens gathers the light from the object and projects a real image within the structure of the optical instrument. A second lens or system of lenses, the eyepiece, then projects a second real image onto the retina of the eye.


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Real image

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A real image is an optical phenomenon in which light rays from an object actually converge at a specific point after passing through an optical system, such as a lens or mirror, forming a visible projection that can be captured on a screen or surface. Unlike virtual images, real images are produced by converging rays and can be projected onto a medium because the light rays physically intersect at the image location. Real images are typically formed by converging lenses or concave mirrors when the object is positioned beyond the focal point of the optical element. In such setups, the lens or mirror bends incoming light rays to focus them at a point on the opposite side of the optical system from the object, resulting in an image distance that is positive in the standard sign convention for optics. For example, in a convex lens, if the object distance exceeds the focal length, the rays converge to form a real image; this principle underlies devices like cameras and projectors. Key properties of real images include their inverted orientation relative to the object—upside down and left-right reversed—and the ability to vary in size depending on the object-to-lens distance, appearing either magnified or reduced. These images are "real" in the sense that they emit or reflect light just as the original object does, allowing them to be observed directly or recorded. In biological systems, the human eye forms a real, inverted image on the retina through the combined action of the cornea and lens, which the brain then interprets as upright. Applications of real images extend to various optical instruments, including slide projectors where enlarged images are cast onto screens, telescopes for distant objects, and microscopes for magnified views, all relying on the precise convergence of to produce clear, projectable visuals. In concave mirrors, real images form similarly when the object is outside the , as seen in certain lighting or solar cooking devices that focus sunlight to a point. Understanding real image formation is fundamental to geometric , enabling advancements in imaging technology and scientific instrumentation.

Definition and Formation

Definition

A real image in is defined as the collection of focused points produced by converging light rays emanating from an object, with the image located at the actual physical plane where these rays intersect after passing through an optical system. This formation contrasts with virtual images, where rays appear to diverge from a point but do not actually converge there. Real images occur only when the incoming rays physically converge to a point, enabling the image to be projected onto a screen, surface, or detector, as the light intensity is concentrated at that location. This property arises within the framework of geometric optics, which approximates propagation as straight-line rays in a homogeneous medium, ignoring wave effects like . The conceptual foundation of real images traces back to 17th-century , where in his 1604 treatise Ad Vitellionem Paralipomena proposed that light rays form a real, inverted image on the , analogous to a . This idea marked a shift from earlier emission theories of vision, establishing real images as tangible optical phenomena. The explicit distinction between real and virtual images was refined in the mid-17th century by scholars including Gilles Personne de Roberval and Jesuit opticians like Francesco Eschinardi and Claude François Milliet Dechales, who integrated Kepler's retinal imaging into broader theories of projection and perception.

Principles of Formation

In converging optical systems, a real image forms when the object distance exceeds the of the system, allowing light rays emanating from the object to converge at a point on the opposite side of the optical element. This condition ensures that the rays, after or reflection, intersect physically rather than diverging. For instance, in a converging lens, placing the object beyond the focal point results in ray convergence behind the lens. The principles of real image formation are illustrated through ray diagrams employing three principal rays originating from a point on the object. The first ray travels parallel to the and, upon interaction with the element, passes through the focal point on the opposite side. The second ray passes through the center of a lens (or strikes a mirror normally) and continues undeflected. The third ray passes through the focal point on the incident side and emerges parallel to the after or reflection. These rays intersect at a single point, defining the location of the point for that object point. Real images are always inverted relative to the object because the principal rays cross each other at the convergence point, reversing the orientation of the image top-to-bottom and left-to-right. This inversion arises inherently from the geometry of ray convergence in converging systems. The represents the surface where all convergence points for an extended object lie, forming a complete . This relies on the paraxial , which assumes rays are near the and make small angles with it, enabling simplified linear equations for ray tracing and minimizing aberrations. These principles apply abstractly to systems like converging lenses and concave mirrors.

Optical Elements Involved

Convex Lenses

A convex lens, also known as a converging lens, forms a real image when the object is placed at a distance greater than the (u > f) from the lens, with the image appearing on the opposite side of the lens from the object. In this configuration, light rays from the object pass through the lens and converge to a point where the image is formed, allowing it to be projected onto a screen. The geometry of real image formation can be illustrated through principal ray diagrams for a convex lens. A ray parallel to the principal optic axis passing through the lens will converge to the focal point on the opposite side after ; meanwhile, a central ray passing through the optical center of the lens remains undeviated. These rays, along with others from the object, intersect to define the position and size of the real image. The characteristics of the produced by a convex lens depend on the object's position relative to the focal point (f) and twice the (2f). If the object is beyond 2f, the is real, inverted, and diminished in size; if the object is between f and 2f, the is real, inverted, and magnified. In both cases, the is inverted relative to the object due to the crossing of light rays. A practical example of real image formation with a convex lens occurs in a camera, where the lens focuses from a distant object (u >> f) onto the , producing a real, inverted, and diminished that is then processed to display the scene upright.

Concave Mirrors

Concave mirrors, which have a reflective surface curved inward, can form real images when the object is positioned beyond the mirror's focal point. In this configuration, incoming light rays from the object reflect off the concave surface and converge on the same side of the mirror as the object, creating a real image that can be projected onto a screen. This occurs because the mirror's curvature causes the reflected rays to focus at a point in front of the mirror, distinct from virtual images formed behind the mirror when the object is closer than the . The formation of the real image can be understood through ray diagrams using principal rays. A ray parallel to the principal axis reflects through the focal point after striking the mirror. Another ray passing through the focal point before reflection emerges parallel to the principal axis afterward. A third ray directed toward the center of curvature reflects back along its original path due to the normal incidence at that point. The intersection of these reflected rays determines the position and size of the real image. These rays illustrate how the concave mirror bends light inward to produce convergence. Real images formed by concave mirrors are always inverted relative to the object. The size of the image varies with the object's distance from the mirror: when the object is beyond the center of curvature (twice the ), the image is diminished and located between the focal point and the center of curvature; when the object is at the center of curvature, the image is the same size as the object; and when the object is between the focal point and the center of curvature, the image is magnified and positioned beyond the center of curvature. These characteristics make concave mirrors suitable for applications requiring focused real images, such as in astronomical telescopes, where a large concave primary mirror forms a real intermediate image of distant celestial objects at its focal plane for further by an .

Properties and Characteristics

Geometric and Optical Properties

Real images in optics are characterized by their geometric properties, which arise from the actual convergence of light rays at a specific point in space. Unlike virtual images, real images are always inverted and laterally reversed relative to the object, meaning the top of the object appears at the bottom of the image, and left and right are swapped. This inversion occurs because the rays from the object cross over during refraction or reflection to form the image on the opposite side of the optical element. Furthermore, due to this physical convergence, real images can be projected onto a screen or surface placed at the image location, where the focused rays create a visible pattern. Optically, real images exhibit higher potential brightness compared to virtual images, as the energy from the light rays is concentrated at the convergence point, increasing the intensity per unit area. However, their clarity is often compromised by aberrations inherent in optical systems. results from the wavelength-dependent of materials, causing different colors to focus at slightly different points and producing color fringing around the image edges. , on the other hand, arises from the varying focal lengths for rays passing through different parts of a lens or mirror, leading to a blurred or hazy , particularly at the periphery. In terms of quantifiable traits, the image distance vv is positive according to the standard in geometric , indicating that the image forms on the opposite side of the optical element from the object. For lenses, the lateral m=vum = \frac{v}{u}, where uu is the object distance (negative in the convention), yields a negative value confirming the inverted orientation. For mirrors, m=−vum = -\frac{v}{u}, also resulting in negative m for real inverted images. A limitation of real images is that they cannot be directly observed by the eye without an intervening screen or detector, as the rays continue to diverge after the convergence point, preventing perception from the image side alone. For instance, convex lenses commonly produce real images when the object is placed beyond the focal point.

Mathematical Description

The mathematical description of real images in relies on fundamental equations derived from geometric principles, applicable to both lenses and mirrors under the paraxial approximation, which assumes rays close to the . These equations quantify the position, size, and orientation of real images formed when light rays converge after or reflection. For thin lenses, the focal length ff is determined by the lens maker's : 1f=(n−1)(1R1−1R2),\frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right), where nn is the of the lens material relative to the surrounding medium, and R1R_1 and R2R_2 are the radii of curvature of the first and second surfaces, respectively (with the that RR is positive if the center of curvature is to the right of the surface). This applies to both convex and concave lenses, yielding a positive ff for converging (convex) lenses that can form real images when the object uu exceeds ff in magnitude. The position of the real formed by a is given by the lens equation, using the Cartesian where distances are measured from the optical center along the axis, with traveling from left to right: object uu is negative for real objects to the left, vv is positive for real images to the right, and ff is positive for converging lenses. The equation is: 1v−1u=1f.\frac{1}{v} - \frac{1}{u} = \frac{1}{f}. For a real , the object must be placed beyond the focal point (∣u∣>f|u| > f), resulting in a positive vv, indicating convergence on the opposite side of the lens. For concave mirrors, which also form real images, the mirror equation is: 1v+1u=1f,\frac{1}{v} + \frac{1}{u} = \frac{1}{f}, with the Cartesian sign convention: uu negative for objects to the left, vv negative for real images to the left of the mirror, and ff negative for concave mirrors (focal point to the left). Real images occur when the object is placed beyond the focal point (∣u∣>∣f∣|u| > |f|), yielding a negative vv, with magnitude either greater or less than ∣u∣|u| depending on the object position relative to the center of curvature, resulting in either enlarged or diminished inverted images. The focal length relates to the radius of curvature RR by f=R/2f = R/2. The lateral magnification mm, defined as the ratio of image height hih_i to object height hoh_o, is given by m=vum = \frac{v}{u} for lenses and m=−vum = -\frac{v}{u} for mirrors. In both cases, the value is negative, indicating that real images are inverted relative to the object, a consequence of the ray paths crossing the axis. For example, in a converging lens setup with u=−3fu = -3f, v=1.5fv = 1.5f, and m=−0.5m = -0.5, producing an inverted, diminished real image. This formula holds under the respective sign conventions. These equations arise from the of paraxial ray diagrams, specifically through the similarity of triangles formed by principal rays. Consider a : one set of similar triangles relates the object height to the deviation at the lens, yielding ho/∣u∣=h′/fh_o / |u| = h' / f, where h′h' is the height at the lens plane (using magnitudes for derivation); another set from the image side gives hi/v=h′/fh_i / v = h' / f. Equating and eliminating h′h' leads to hi/ho=v/uh_i / h_o = v / u, and extending to the full paths derives the lens . Similar triangular relations to mirrors, confirming the mirror equation for paraxial approximations where sin⁡θ≈θ\sin \theta \approx \theta.

Comparison and Applications

Comparison with Virtual Images

Real images are formed by the actual convergence of light rays at a specific location after passing through an optical element, such as a converging lens or concave mirror, resulting in a projectable that is typically inverted relative to the object. In contrast, virtual images arise from diverging rays that only appear to originate from a point, without actual convergence, and are usually upright. The formation of a real occurs when the object is positioned beyond the (f) of the optical element, allowing rays to cross and form the image on the opposite side. Virtual images form when the object is within the for converging elements, like in a , or with diverging elements, where rays do not cross but seem to extend backward. In the standard sign convention for lens and mirror equations, the image distance (v) is positive for real images, indicating formation on the opposite side of the optical element from the object, while it is negative for virtual images, signifying the same side. This convention aligns with the Cartesian system where light travels from left to right, distinguishing real images by their positive v value in calculations. Real images are observable only when projected onto a screen or surface at the convergence point, as the rays physically meet there, whereas virtual images cannot be projected and are viewed directly by the eye looking through the optical element, relying on the apparent ray paths.

Practical Applications

In cameras, a convex lens converges light rays from an object to form a real, inverted image on the focal plane, where it is captured by a digital sensor or photographic film, enabling the recording and reproduction of visual scenes. This process relies on the lens being positioned such that the object distance exceeds the focal length, ensuring the image is real and projectable onto the recording medium. Projectors utilize converging to create enlarged real images projected onto screens, where from an illuminated slide, , or digital source passes through a lens system to form a focused at a distant plane. This application inverts and magnifies the source material for viewing by an audience, with the screen serving as the where rays actually converge. In compound microscopes and telescopes, the objective lens forms a real intermediate of the specimen or distant object near its focal plane, which the then magnifies further to produce a larger final for . This two-stage process allows for high while maintaining focus, with the intermediate real enabling precise alignment in optical instruments. The employs its crystalline lens to form a real, inverted image on the , where photoreceptor cells convert the optical signal into neural impulses for , and accommodation—via contraction—adjusts lens curvature to focus objects at varying distances from about 25 cm to . Advancements in and since 2020 have leveraged meta-lenses to generate compact, high-fidelity real images for 3D projections, such as in eyepieces that achieve wide fields of view exceeding 60 degrees while forming focused images without bulky . These meta-optical systems enable immersive 3D displays by precisely controlling wavefronts to converge light into real image planes, enhancing applications in and .

References

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  3. https://pressbooks.online.ucf.edu/phy2053bc/chapter/image-formation-by-lenses/
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  5. http://hyperphysics.phy-astr.gsu.edu/hbase/Class/PhSciLab/imagei.html
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  11. http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/raydiag.html
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  22. https://www.feynmanlectures.caltech.edu/I_27.html
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  25. http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/lenseq.html
  26. https://www.st-andrews.ac.uk/~bds2/optics/cartesian.html
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  36. https://web.physics.ucsb.edu/~lecturedemonstrations/Composer/Pages/80.42.html
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