There's an inverse relationship between object size and the maximum angle at which light is scattered. As illustrated in Fig.1, objects that are small relative to the wavelength of incoming light scatter the light across wider angles than larger objects. For clarity, the light that didn't interact with the sample is excluded from the drawing in Fig.1. At extremely small particle sizes, scattered light leaves the object in all directions. This means the smaller the detail in a structure we're trying to resolve, the greater the spread of light coming from it.

The range of angles that a microscope objective can collect is represented by its numerical aperture (NA). There are two key determining factors for NA - the refractive index (n) of the medium between the objective and the sample, and the size of the objective lens aperture. The size of the aperture controls the range of angles that can be transmitted to the detector. Fig.2 illustrates the optical path of a modern infinity-corrected microscope for different size apertures.

If microscopes are imaging through dense mediums such as oil, the refractive index (n) is greater, and the higher the NA. This is why higher magnification lenses often use oil and other immersion objectives.

Magnifying glasses typically have low magnifying power: 2×–6×, with the lower-power types being much more common. At higher magnifications, the image quality of a simple magnifying glass becomes poor due to optical aberrations, particularly spherical aberration. When more magnification or a better image is required, other types of hand magnifier are typically used. A Coddington magnifier provides higher magnification with improved image quality. Even better images can be obtained with a multiple-lens magnifier, such as a Hastings triplet. High power magnifiers are sometimes mounted in a cylindrical or conical holder with no handle, often designed to be worn on the head; this is called a loupe.

Cameralens magnification

Schermelleh L., Ferrand A., Huser T., Eggeling C., Sauer M., Biehlmaier O. and Drummen GPC. 2019 Super-Resolution microscopy demystified. Nature Cell BIolog v21:72 72-84

A single photon could fall anywhere within the PSF, but if 100 photons are collected from a single point source, the localization precision could increase by a factor of 10. In the example used previously, where the resolution was 250 nm for a perfect air lens, collecting 100 photons from a unique point source, allows the center to be localized within 25 nm. This means with many photons, we could determine the location of point sources within the sample with great precision and resolve finer details.

For the example given earlier of a diffraction-limited resolution of 320 nm, one would need pixels sampling every 140 nm in the image to truly achieve this resolution. With a 6.5 µm pixel, 45-50x magnification would provide pixels of an appropriate size. Magnification has no influence on the optical blur of the microscope but does allow appropriate sampling to recover all the information transmitted by the microscope.

The NA is calculated from the refractive index in front of the objective and the half-angle (θ) of light that the lens transmits from the sample towards the detector.

Zoomlens magnification

Fig.4 illustrates a case where the sensor's large pixels undersample the spatial information in the neuron. Using smaller pixels or increasing the magnification solves the problem.

"The evidence indicates that the use of lenses was widespread throughout the Middle East and the Mediterranean basin over several millennia".[1] Archaeological findings from the 1980s in Crete's Idaean Cave unearthed rock crystal lenses dating back to the Archaic Greek period, showcasing exceptional optical quality. These discoveries suggest that the use of lenses for magnification and possibly for starting fires was widespread in the Mediterranean and Middle East, indicating an advanced understanding of optics in antiquity.[2] The earliest explicit written evidence of a magnifying device is a joke in Aristophanes's The Clouds[3] from 424 BC, where magnifying lenses to ignite tinder were sold in a pharmacy, and Pliny the Elder's "lens",[4] a glass globe filled with water, used to cauterize wounds. (Seneca wrote that it could be used to read letters "no matter how small or dim".[5][6]) A convex lens used for forming a magnified image was described in the Book of Optics by Ibn al-Haytham in 1021.[7][verification needed] After the book was translated during the Latin translations of the 12th century, Roger Bacon described the properties of a magnifying glass in 13th-century England. This was followed by the development of eyeglasses in 13th-century Italy.[7] Building on this foundation, in the late 1500s, two Dutch spectacle makers Jacob Metius and Zacharias Janssen crafted the compound microscope by assembling several magnifying lenses in a tube, marking a significant advancement in optical instruments. Not long after, Hans Lipperhey introduced the telescope in 1608 and Galileo Galilei improving on the device in 1609, employing the magnifying lens in an innovative manner, further extending the application of optical technologies developed through the ages.[8]

The highest magnifying power is obtained by putting the lens very close to one eye, and moving the eye and the lens together to obtain the best focus. The object will then typically also be close to the lens. The magnifying power obtained in this condition is MP0 = (0.25 m)Φ + 1, where Φ is the optical power in dioptres, and the factor of 0.25 m represents the assumed near point (¼ m from the eye). This value of the magnifying power is the one normally used to characterize magnifiers. It is typically denoted "m×", where m = MP0. This is sometimes called the total power of the magnifier (again, not to be confused with optical power).

A magnifying glass can serve as a fire-starting tool in survival situations. Any transparent lens with significant magnifying ability, such as a standard magnifying glass or a jeweler's loupe, can concentrate sunlight to ignite tinder. The technique involves positioning the lens to focus a small, intense spot of light onto the tinder, awaiting ignition with patience. The advantage of this method is the simplicity of the lens and the minimal effort required. However, its effectiveness is contingent upon clear, strong sunlight, which may be inconsistent depending on geographic location and time of year.[11]

A magnifying glass is a convex lens that is used to produce a magnified image of an object. The lens is usually mounted in a frame with a handle. Beyond its primary function of magnification, this simple yet ingenious tool serves a variety of purposes. It can be employed to focus sunlight, harnessing the Sun's rays to create a concentrated hot spot at the lens's focus, which is often used for starting fires.

Figure 3 was derived from the Immersion tutorial on Nikon's MicroscopyU website (https://www.microscopyu.com/tutorials/immersion)

The more open the aperture, the more angles of light that can pass through the lens to the sample, and the higher the NA. At its largest, the angle would be defined by the radius and focal length of the lens itself, but many objectives are made with smaller back apertures to control for aberrations at the periphery of lenses and other issues.

2021330 — This article is part 2 of the series focusing on how to use the Paraxial Gaussian Beam analysis tool to model Gaussian beam.

As a single point of light is diffraction-limited and spreads out before meeting the sample, the image of a point on the sample is blurred. This blur is known as the point spread function (PSF) and has a characteristic shape known as an Airy disk, as illustrated in the map of intensity vs position shown in Fig.5.

201774 — Entwickelt für 6 Megapixel CCD Sensoren! Features Hohe Leistung von Makro bis Unendlich Sehr gute Eignung für den industriellen Einsatz und ...

In another innovative form, the magnifying glass can manifest as a sheet magnifier, employing numerous slender, concentric, ring-shaped lenses. These are collectively known as a Fresnel lens, which, despite being significantly thinner, operates effectively as a single lens. This particular design finds its utility in applications such as screen magnifiers for TVs, offering a lightweight and efficient solution for enlarging visuals.

Macrolens magnification

Mar 18, 2021 — We use different hard coating materials over foam to protect it. Some include epoxy, polyurea, rubber latex and polyurethane coatings.

The cultural impact of the magnifying glass extends far into the realms of literature and pop culture, symbolizing the pursuit of truth and the uncovering of secrets. It is famously associated with the investigative work of fictional detectives, with Sherlock Holmes being the most iconic figure to wield it, cementing its status as an emblem of detective fiction. Through its various forms and functions, the magnifying glass remains a tool of both practical utility and significant symbolic value.

This Airy disk has most of the light power distributed in the central lobe, with lower amounts distributed to secondary lobes. If the area of the center of the peak can be located with greater precision, this can indicate the location of the point source. The precision with which one can localize the center of the PSF generated by a single point source depends on the number of photons detected from that source.

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For transmitted light techniques, the diffraction behavior is determined by the scattering of light from features in the sample. Scattering occurs when light encounters a change in refractive index, such as at the interface of an object. The refractive index, n, is a measure of how much light slows as it passes through the material of that object. The speed of light is a constant in a vacuum, but slower in materials denser than a vacuum. Common refractive indexes are 1.0 for vacuum, 1.33 for water, 1.37-1.39 for biological materials, 1.57 for glass and a number just slightly greater than 1.0 for air.

Camera pixel size should be matched to the diffraction-limited blur. In order to differentiate between two objects, one must make a measurement in between them. By convention, the pixel size needs to be 1÷2.3 (~0.44) as large as the smallest object to be imaged. If the smallest object in a sample is 1 µm, the pixel size should be at least 0.44 µm in order to best image the sample. Pixel sizes larger than this will lose information, known as undersampling, while pixel sizes smaller than this provide no extra information, known as oversampling.

Maximummagnificationcameralens

When light travels between mediums with different refractive indexes at an angle, the light slows and is bent, this is refraction. Typically this occurs when light emitted from the sample hits a glass-air interface. As illustrated in Fig.3, when air fills the interface gap between sample and objective, the higher angles are bent at the interface and fail to be collected by the objective. In contrast, when oil (much higher refractive index) fills the gap, light is bent less and is all collected by the objective.

An often-asked question in imaging is whether two objects are in the same or separate places. Resolution, the ability to tell two nearby features apart, is a key parameter of microscope optics that becomes more challenging at smaller length scales. Yet, this has surprisingly little to do with the microscope's ability to magnify. In this technical note, the underlying principles that define resolving power, and the conditions necessary to achieve that resolution in a microscope image, are considered.

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Jul 11, 2019 — The focal length defines the magnification and field of view for a given lens. This value is most commonly measured in millimeters. Prime lenses ...

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The total magnification (M) of the optical system makes objects in the sample appear M times larger at the camera. For example, a microscope camera might have 2000×2000 pixels with each pixel measuring 6.5 µm by 6.5 µm. Depending on the magnification, the pixel will sample different regions in the sample. Using a 10x lens, one 6.5 µm by 6.5 µm pixel would sample 650 nm by 650 nm of the sample. In contrast, using a 100x lens that same pixel would sample 65 nm by 65 nm.

Figure 5 was derived from Numerical Aperture and Resolution on the Nikon MicroscopyU website (https://www.microscopyu.com/tutorials/imageformation-airyna)

In most mobile hidden object games, the magnifying glass, used as a hint or booster, helps players locate items by highlighting or zooming in on them, making hidden objects easier to spot and enhancing gameplay accessibility.

Beyond its digital symbolization for search functions, the magnifying glass also holds a place in educational symbolism, often representing curiosity, exploration, and the quest for knowledge. Educational institutions and programs frequently use the magnifying glass in logos and materials to emphasize the importance of inquiry and discovery in learning.[15]

So why does the emission of light in all directions influence resolution? The limiting factor of microscope resolution is how broad a range of angles of light from the sample the microscope objective can collect. For example, if a small object scattering light at a wide range of angles was imaged using a microscope objective, only a subset of that light would be collected - this would be indistinguishable from a larger object emitting a narrower range of angles. This 'coarsening' of length scale displays as blurring of the microscope image.

If you need to know the threads per inch of a metric fastener, first convert pitch from millimeters to inches (multiply by 0.03937), then divide 1 by that ...

However, magnifiers are not always used as described above because it is more comfortable to put the magnifier close to the object (one focal length away). The eye can then be a larger distance away, and a good image can be obtained very easily; the focus is not very sensitive to the eye's exact position. The magnifying power in this case is roughly MP = (0.25 m)Φ.

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Microscope imaging can typically be split into transmitted light techniques where light passes through a sample from a source opposite the objective lens, and fluorescence-based techniques where light is re-emitted from the sample due to an interaction with light. In both cases, the microscope's ability to differentiate fine details is limited by the diffraction behavior of light waves. Diffraction causes the light from the sample to spread out, and this spreading limits our ability to resolve.

However, this localization works only when we know that the photons within the PSF come from only one point source - which is not the case in conventional microscopy where fluorescent molecules are far more densely packed than the PSF size. Controlling the conditions so that single point sources can be imaged in a sample consisting of many point sources underpins PALM/STORM super-resolution microscopy techniques (Schermelleh et al. 2019 for review).

Figures 1 is taken from the Particle Size Analysis blog on Laser Light Scattering (https://technologypharmaceutical.wordpress.com/2014/12/10/laser-light-scattering-method/)

Our ability to image fine details in microscopy is limited by the resolving power of the microscope and of the camera. The microscope resolution is determined by the numerical aperture of the objective, which depends on the refractive index of immersion medium used, and the size of the back aperture of the objective, combined with the wavelength of light from the sample.

The magnification of a magnifying glass depends upon where it is placed between the user's eye and the object being viewed, and the total distance between them. The magnifying power is equivalent to angular magnification (this should not be confused with optical power, which is a different quantity). The magnifying power is the ratio of the sizes of the images formed on the user's retina with and without the lens.[9] For the "without" case, it is typically assumed that the user would bring the object as close to one eye as possible without it becoming blurry. This point, known as the near point of accommodation, varies with age. In a young child, it can be as close as 5 cm, while, in an elderly person it may be as far as one or two metres. Magnifiers are typically characterized using a "standard" value of 0.25 m.

Figures 2 & 4 were derived from the lecture notes of Dr. Jerome Mertz' BE517 class at Boston University and modified for clarity.

Fluorescent molecules emit in many directions. When examined in bulk, fluorescent molecules typically radiate light in all directions. Although individual fluorescent molecules can emit photons in a small range of angles, with the influence of molecular movement even single fluorescent molecules can be considered to be emitting in all directions.

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A perfect air lens, meaning the gap between the front element of the objective and the sample is filled with air, can have a maximum NA of around 1.0 due to the refractive index of air. To achieve higher NA, it is necessary to fill the space between the objective and the sample with immersion media with n greater than 1.0, such as water (n=1.33), glycerol (n=1.46) or immersion oil (n=1.51).

Beyond survival uses, magnifying glasses are invaluable tools for jewelers and hobbyists. Jewelers rely on them to scrutinize the quality and authenticity of precious gems, ensuring accurate evaluations. Hobbyists, from those engaged in sewing and needlework to stamp collectors, depend on magnifying glasses for detailed work, enhancing both precision and enjoyment. This versatility underlines the magnifying glass's enduring utility across a spectrum of activities, from professional assessments to leisure pursuits.[8]

Diffraction-limited imaging defines the size of the smallest objects in the image. Anything smaller will be blurred by the microscope to the diffraction-limited size. Since the diffraction limit is set by the NA of the objective and the wavelength of light used, it may be mistakenly assumed that we are always performing diffraction-limited imaging. However, this is not necessarily true depending on the size of the camera's pixel and the magnification of the system.

Advanced digital magnifiers and apps have emerged as modern alternatives to traditional magnifying glasses, offering features such as variable magnification levels, high-contrast modes, and text-to-speech for visually impaired users. These tools not only magnify text and objects but also enhance readability and accessibility, making them invaluable for daily living and educational purposes.[12][13]

Lens magnificationChart

A magnifying glass operates as the simplest form of optical instrument. It is essentially a hand-held lens that converges light to produce an enlarged, upright image that appears to stand where light doesn't actually converge, known as a 'virtual' image. To view an item in greater detail, it is positioned between the lens and its focal point, and the optimal observation occurs when the image is at the closest distance at which the eye can focus comfortably. The lens's magnification is the ratio of the image's apparent height to the object's actual height, correlating to the proportion of the distances from the image to the lens and the object to the lens. Moving the object nearer to the lens amplifies this effect, increasing magnification.[10]

A typical magnifying glass might have a focal length of 25 cm, corresponding to an optical power of 4 dioptres. Such a magnifier would be sold as a "2×" magnifier. In actual use, an observer with "typical" eyes would obtain a magnifying power between 1 and 2, depending on where lens is held.

Aug 2, 2021 — In more technical terms, depth of field is the distance in an image where objects appear acceptably in focus or have a level of acceptable ...

Such magnifiers can reach up to about 30×, and at these magnifications the aperture of the magnifier becomes very small and it must be placed very close to both the object and the eye. For more convenient use or for magnification beyond about 30×, a microscope is necessary.

Lens magnificationcalculator

In general, the larger the back aperture the wider the angles we can collect, the larger the NA, and the higher the resolution. The theoretical maximum angle that light can be collected by a lens is 180 (it would have to be a huge lens), making the maximum half-angle 90. Realistically, half-angles above 72 cannot currently be achieved. For an air lens with half-angle 72, the NA would then be 0.95 and the maximum resolution (the smallest object that could be observed) of the image would be 320 nm. Two objects closer than 320 nm would not be resolved and would appear as one object, and anything smaller than 320 nm would appear as a blurry blob 320 nm in size. This is the diffraction limit to imaging.

The maximum resolving power of an optical system is defined by the following: how close together can two small features be such that the blurring of their images doesn't lead to them appearing as one feature? This is a loose definition that depends on the wavelength of light used.

The magnifying glass icon (🔍), represented by U+1F50D in Unicode, has evolved into a universal symbol for searching and zooming functions in digital interfaces. Originating from its practical use for detailed examination and discovery, it has been adopted by modern computer software and websites to denote tools for users to find information or closely inspect content.[9][10] The right-pointing version, U+1F50E (🔎), continues this theme, often used to initiate searches. The integration of these icons into user interface design reflects the intuitive connection between the physical act of magnifying to see more clearly and the metaphorical act of searching for information in the digital space.[14]

For thin samples mounted with index-matching medium, the glass and sample can be considered to have the same refractive index. When sample thickness increases, or where no index-matching medium can be used (live cell imaging), choosing immersion objectives that use water or glycerol as index matching fluids, being similar to the sample, can be more effective.