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Virtual image
Virtual image
Virtual image
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The formation of the virtual image A' of the object A via a plane mirror. For people looking at the mirror, the object A is apparently located at the position of A' although it does not physically exist there. The magnification of the virtual image formed by the plane mirror is 1.
Top: The formation of a virtual image using a diverging lens. Bottom: The formation of a virtual image using a convex mirror. In both diagrams, f is the focal point, O is the object, and I is the virtual image, shown in grey. Solid blue lines indicate (real) light rays and dashed blue lines indicate backward extension of the real rays.

In optics, the image of an object is defined as the collection of focus points of light rays coming from the object. A real image is the collection of focus points made by converging rays, while a virtual image is the collection of focus points made by backward extensions of diverging rays. In other words, a virtual image is found by tracing real rays that emerge from an optical device (lens, mirror, or some combination) backward to perceived or apparent origins of ray divergences.[1]

There is a concept virtual object that is similarly defined; an object is virtual when forward extensions of rays converge toward it.[1] This is observed in ray tracing for a multi-lenses system or a diverging lens. For the diverging lens, forward extension of converging rays toward the lens will meet the converging point, so the point is a virtual object.

For a (refracting) lens, the real image of an object is formed on the opposite side of the lens while the virtual image is formed on the same side as the object. For a (reflecting) mirror, the real image is on the same side as the object while the virtual image is on the opposite side of, or "behind", the mirror. In diagrams of optical systems, virtual rays (forming virtual images) are conventionally represented by dotted lines, to contrast with the solid lines of real rays.

Because the rays are not actually present at the apparent location, and thus never really converge at any point, a virtual image cannot be projected onto a screen by putting it at the location of the virtual image. In contrast, a real image can be projected on the screen as it is formed by rays that converge on a real location. A real image can be projected onto a diffusely reflecting screen so people can see the image (the image on the screen plays as an object to be imaged by human eyes).[2]

  • A plane mirror forms a virtual image positioned behind the mirror. Although the rays of light seem to come from behind the mirror, light from the source only exists in front of the mirror. The image in a plane mirror is not magnified (that is, the image is the same size as the object) and appears to be as far behind the mirror as the object is in front of the mirror.
  • A diverging lens (one that is thicker at the edges than the middle) or a concave mirror forms a virtual image. Such an image is reduced in size when compared to the original object. A converging lens (one that is thicker in the middle than at the edges) or a convex mirror is also capable of producing a virtual image if the object is within the focal length. Such an image will be magnified. In contrast, an object placed in front of a converging lens or concave mirror at a position beyond the focal length produces a real image. Such an image will be magnified if the position of the object is within twice the focal length, or else the image will be reduced if the object is further than this distance.

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Virtual image

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A virtual image is an in which light rays from an object diverge after passing through an optical system, appearing to originate from a point that does not lie on the actual path of the rays. Unlike a , where rays converge to a physical point that can be projected onto a screen, a virtual image cannot be so projected and is located where the backward extensions of the diverging rays intersect. This apparent location makes virtual images observable only through the optical device itself, such as by direct viewing. Virtual images form in various optical setups involving mirrors and lenses. With mirrors, plane mirrors always produce virtual images located behind the reflecting surface at an equal distance from the object, resulting in an erect image of the same size. Convex mirrors exclusively form virtual images that are upright and reduced in size, providing a broader field of view. Concave mirrors generate virtual images only when the object is positioned between the mirror and its focal point, yielding an enlarged, erect image. For lenses, diverging lenses consistently create virtual images on the same side as the object, which are upright and smaller. Converging lenses produce virtual images when the object is closer than the focal length, forming an enlarged, upright image on the same side of the lens as the object. Key characteristics of virtual images include their erect orientation relative to the object and their negative image distance in the standard sign convention of geometrical optics. These properties arise from the divergence of rays, as described by the lens or mirror equation, where the image distance is negative. In practical applications, virtual images enable everyday uses like the reflection in a bathroom mirror or the wider-angle view in a vehicle's convex rearview mirror, which displays an upright but diminished image for safety. They also form the basis for magnification in simple optical instruments, such as a handheld magnifying glass, where the enlarged virtual image aids in detailed viewing.

Definition and Properties

Definition

A virtual image in optics is formed when incoming light rays, after interacting with an optical element such as a mirror or lens, diverge in such a way that they appear to an observer to be emanating from a specific point, but no actual light rays converge or originate at that apparent location. This apparent source, often positioned behind the optical element relative to the observer, serves as the perceived origin of the light, creating the illusion of an image without any physical projection or focus of rays there. To understand this concept, consider that propagates in straight-line paths called rays, which the traces back to determine the direction and position of objects. When rays diverge after reflection or , the eye perceives their extensions backward along these paths to a virtual point, forming the ; this differs from real images, where rays physically converge to a tangible point that can be captured on a screen. The foundational understanding of virtual images emerged within , first systematically described by the 11th-century scholar (known as Alhazen) in his seminal work, the , where he analyzed ray paths and apparent image positions in reflective and refractive systems.

Key Properties

Virtual images exhibit several distinctive properties that arise from the apparent intersection of diverging light rays. Unlike converging rays that form real images, the rays in a virtual image setup diverge after interaction with an optical element, requiring the observer's eye to trace them backward to their perceived origin. This perceptual formation means virtual images exist only in the observer's perception and cannot be captured on a physical medium without additional . A fundamental property of virtual images is their upright orientation relative to the object, meaning they appear erect without inversion. This erect nature holds across various optical systems, such as plane mirrors, convex mirrors, diverging lenses, and converging lenses when the object is within the . The magnification of virtual images can vary: they may be enlarged, as in a magnifying glass using a converging lens; reduced in size, typical of diverging lenses or convex mirrors; or the same size, as seen in plane mirrors. In the Cartesian of , virtual s are characterized by a negative . Virtual s are located on the side of the optical element from which is incident, appearing "behind" the mirror or lens from the observer's viewpoint. For mirrors, this places the image behind the reflecting surface; for lenses, it positions the image on the object side. Due to the diverging nature of the rays, virtual s cannot be projected onto a screen, as no actual convergence occurs at the image location—any screen placed there would show no focused image. This non-projectable quality underscores their perceptual essence, relying entirely on the observer's interpretation of ray directions.

Formation in Optical Systems

In Mirrors

In plane mirrors, virtual images are formed when incident rays from an object reflect off the flat surface and diverge as if emanating from a point behind the mirror. The image appears at an equal distance behind the mirror as the object is in front, maintaining the same size and orientation (upright). This occurs because the reflected rays are parallel to the incident rays but reversed in direction, and the observer's eye traces them backward to their apparent intersection point. A typical ray diagram illustrates this by drawing two rays from the object top: one normal to the mirror reflects back on itself, while another at an angle reflects with equal incidence and reflection angles, both appearing to diverge from the virtual image location behind the mirror. Convex mirrors produce virtual images for all object positions due to their diverging reflection, where rays from the object spread out after reflection and appear to originate from a point behind the mirror. These images are always upright and diminished in size compared to the object, providing a wider because the diverging rays cover a broader angular extent. For example, in rearview mirrors of , this property allows observation of a larger area behind the driver. In concave mirrors, virtual images form only when the object is placed inside the focal point, where the converging reflection causes rays to diverge after bouncing off the surface, appearing to come from an upright, magnified image behind the mirror. Beyond the focal point, real images form instead. The position and nature of these images are calculated using the mirror formula: 1v+1u=1f\frac{1}{v} + \frac{1}{u} = \frac{1}{f} Here, uu is the object distance (positive for objects in front of the mirror), vv is the image distance (negative for virtual images behind the mirror), and ff is the (positive for concave mirrors, negative for convex mirrors). This derives from the geometry of spherical mirrors under paraxial approximation. The sign convention used is the real-positive convention, where distances are positive if on the side opposite to the incoming light for real objects and images, and negative if on the incoming light side for virtual cases. Object distance uu is positive for real objects in front of the mirror. Image distance vv is positive for real images in front of the mirror and negative for virtual images behind the mirror. Focal length ff is positive for concave (converging) mirrors and negative for convex (diverging) mirrors. This convention ensures accurate predictions of image location and type across mirror types.

In Lenses

In lenses, virtual images form through the of rays as they pass through the lens material, causing the rays to appear to diverge from or converge to a point on the same side of the lens as the object, without actually meeting there. This process differs from reflection in mirrors by involving transmission and bending at the lens surfaces rather than bouncing back. For concave (diverging) lenses, which have a negative , virtual images are always produced when a real object is placed on the incident side. The refracted rays diverge after passing through the lens, and their backward extensions intersect at an apparent point behind the lens (on the object side), forming an upright and diminished relative to the object. This occurs for any object distance greater than zero, as the diverging nature spreads the rays without allowing convergence on the opposite side. In convex (converging) lenses, which have a positive , virtual images form only when the object is positioned inside the (closer to the lens than the focal point). Here, the refracted rays diverge after the lens, but their backward extensions converge to an apparent point on the object side, resulting in an upright and magnified . For objects beyond the , converging lenses typically produce real images instead. The formula governs location in these cases, approximated for lenses where thickness is negligible compared to : 1v−1u=1f\frac{1}{v} - \frac{1}{u} = \frac{1}{f} where uu is the object (positive for objects on the incident side), vv is the (negative for virtual images on the incident side), and ff is the (positive for converging, negative for diverging). For virtual images, the negative vv value indicates the position on the object side. This equation, derived from paraxial ray approximation, allows calculation of properties assuming small angles and indices of differences at the interfaces. Ray diagrams illustrate these formations using principal rays. For a diverging lens, one ray parallel to the axis refracts away as if from the focal point on the object side; another through the center passes undeviated; their extensions meet behind the lens at the virtual image. In the converging lens case with object inside , the parallel ray refracts through the opposite focal point but extends backward to diverge; the central ray remains straight; extensions intersect on the object side for the enlarged virtual image. These diagrams confirm the image's upright orientation and position without actual ray convergence.

Comparison with Real Images

Formation Differences

Real images are formed when light rays from an object actually converge at a specific point after interacting with an optical element, such as a lens or mirror, creating a location where the rays intersect in physical space. In contrast, virtual images arise from the apparent divergence of light rays, where the rays do not physically meet but appear to emanate from a point when traced backward, resulting in an illusory origin behind or within the optical system. This fundamental distinction in ray behavior—actual convergence versus perceived divergence—underlies the differing formation mechanisms in optical systems. The conditions for forming real versus virtual images depend on the type of optical system and the object's position relative to the focal point. In converging (positive ) systems, like convex lenses or concave mirrors, a real image forms when the object is placed beyond the focal point, allowing rays to cross after or reflection. Conversely, virtual images occur in diverging (negative ) systems, such as concave lenses or convex mirrors, where rays always diverge regardless of object position, or in converging systems when the object is inside the focal point, causing rays to diverge after interaction. For instance, in a converging lens, an object within the focal length produces a virtual image on the same side as the object. A key physical implication of these formation differences is the absence of energy concentration in virtual images. Real images involve light rays converging at the image point, leading to a buildup of optical that can expose or cause heating if intense. Virtual images, however, lack this convergence, so no accumulates at the apparent image location; placed there remains unexposed, as the rays do not pass through that point. This energy disparity highlights why real images can be captured or projected, while virtual ones require direct viewing to perceive.

Observability and Detection

Virtual images are perceived by an observer's eye, which traces back the diverging rays to their apparent point of origin, creating the of an at that location. Unlike real images, virtual images cannot be captured or projected onto a screen because the rays do not actually converge there, resulting in no tangible projection. Detection of virtual images relies on methods that verify their apparent position without physical convergence, such as measurement, where the observer shifts their viewpoint to check for relative motion between the image and a reference object. If no relative motion (no ) is observed, the reference aligns with the virtual image's location. Additionally, there is no concentration of , , or intensity at the virtual image point, distinguishing it from real images where rays focus and produce measurable effects. A common experimental setup to demonstrate and locate a virtual image uses a and a pin as the object placed in front of it. A second pin, serving as the reference, is positioned behind the mirror and adjusted until it coincides with the virtual image of the first pin, confirmed by the absence of when the observer moves their head side to side. This method precisely determines the image's apparent position at an equal distance behind the mirror. Virtual images are inherently observer-dependent, as their relies on the viewer's eye position and ray tracing, and in simple optical setups like a single , they cannot effectively serve as objects for subsequent stages due to the lack of actual convergence.

Examples and Applications

Everyday Examples

In vehicles, convex rearview mirrors create virtual images of objects behind the driver, appearing smaller and farther away to provide a broader and reduce blind spots for enhanced . These mirrors form the image through of reflected rays, ensuring an upright and diminished appearance regardless of the object's position. Plane mirrors, such as those used in dressing tables or bathrooms, produce life-size virtual images that appear directly behind the mirror surface at the same distance as the observer, facilitating by allowing accurate assessment of appearance. This setup ensures the image remains upright and laterally inverted, aiding in tasks like adjusting clothing or hairstyles. Retail stores employ convex security mirrors at aisle ends to generate virtual images that encompass a wide area without obstructions, enabling staff to monitor customer activity and prevent theft effectively. The resulting images are erect and reduced in size, prioritizing coverage over detail in everyday monitoring scenarios. A simple household item like a demonstrates virtual image formation on its concave inner surface; when held close to the face—within the short —the reflection appears as an enlarged, upright virtual behind the spoon. This occurs because the object distance is less than the , causing reflected rays to diverge and form the image through apparent extension backward.

In Optical Instruments

Virtual images play a central role in many optical instruments by allowing the to observe enlarged or distant objects without the need for a physical screen, as the image is formed by the apparent divergence of light rays. In these devices, the final image is typically virtual, meaning it cannot be projected onto a surface and is viewed directly through an or lens, enhancing angular magnification for the observer. This configuration is essential for instruments like simple magnifiers, compound microscopes, and telescopes, where the virtual image is positioned at or near the eye's (about 25 cm) or at for relaxed viewing. In a simple magnifier, also known as a , a single converging lens forms an enlarged, upright virtual image of a nearby object placed within the lens's . The object distance is less than the ff, causing the rays to diverge after passing through the lens, with the virtual image appearing farther away and larger than the object. Angular magnification mm is given by m=25f+1m = \frac{25}{f} + 1 when the image is at the , where ff is in centimeters, allowing the eye to resolve finer details than unaided vision. For relaxed viewing, the image is at , and m=25fm = \frac{25}{f}. This setup increases the apparent size by subtending a larger at the eye compared to viewing the object directly at 25 cm. Compound microscopes utilize two converging lenses to achieve high magnification of small, close objects. The objective lens, with a short focal length (typically a few millimeters), forms an enlarged real intermediate image just beyond its focal point. This intermediate image then serves as the object for the eyepiece, which acts as a simple magnifier to produce a final virtual image at the near point or infinity. The total angular magnification is approximately m=−Lfo×25fem = -\frac{L}{f_o} \times \frac{25}{f_e}, where LL is the tube length (often 16 cm or 20 cm), fof_o is the objective focal length, and fef_e is the eyepiece focal length, yielding magnifications up to 1000× or more. The final virtual image is inverted relative to the object and appears to float in space within the microscope tube, enabling detailed observation of microscopic structures. Telescopes extend the simple magnifier principle to distant objects, using an objective lens or mirror to collect light and form a real intermediate image at its focal plane. The eyepiece then views this image, creating a final virtual image at infinity for comfortable viewing with a relaxed eye. In the Keplerian telescope, both lenses are converging, resulting in an inverted virtual image with angular magnification m=−fofem = -\frac{f_o}{f_e}, where fof_o and fef_e are the objective and eyepiece focal lengths, respectively; typical values provide magnifications of 10× to 100×. The Galilean telescope uses a diverging eyepiece, producing an erect virtual image without inversion, though with a narrower field of view. This virtual image formation allows the eye to perceive remote objects as if they were nearby and enlarged.

References

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