We encourage you to check similar cases for the diverging lens, which has a negative focal length f < 0 with our calculator!

The magnification of a lens is the ratio of the size of the image to the size of the object. Hence, to find the magnification of a lens, take the ratio of the two. You can also calculate magnification by taking the ratio of the image-lens distance to the object-lens distance.

There are two basic types of lenses. We can distinguish converging lenses, which have focal length f > 0, and diverging lenses for which focal length f < 0. It should also be noted that when the image distance is positive y > 0, then the image appears on the other side of the lens, and we call it a real image. On the other hand, when y < 0, then the image appears on the same side of the lens as the object, and we call it a virtual image.

Focal lengthof mirror formula

You can compute the magnification of the created image, too (see the mirror equation calculator). It can be easily estimated if we know the distance of object x and the distance of image y:

Let us consider five different situations for a converging lens (f > 0). You can check it with our thin lens equation calculator!

DIC is used for imaging live and unstained biological samples, such as a smear from a tissue culture or individual water borne single-celled organisms. Owing to the maximally spatially incoherent illumination the theoretical resolution approaches the theoretical maximum coverage dictated by Ewald's sphere.[4] This is an improvement on methods that require a higher degree of coherence like phase contrast.

The contrast can be adjusted using the offset phase, either by translating the objective Nomarski prism, or by a lambda/4 waveplate between polarizer and the condenser Normarski prism (De-Senarmont Compensation). The resulting contrast is going from dark-field for zero phase offset (intensity proportional to the square of the shear differential), to the typical relief seen for phase of ~5–90 degrees, to optical staining at 360 degrees, where the extinguished wavelength shifts with the phase differential.

Lens makerequation

The typical phase difference giving rise to the interference is very small, very rarely being larger than 90° (a quarter of the wavelength). This is due to the similarity of refractive index of most samples and the media they are in: for example, a cell in water only has a refractive index difference of around 0.05. This small phase difference is important for the correct function of DIC, since if the phase difference at the joint between two substances is too large then the phase difference could reach 180° (half a wavelength), resulting in complete destructive interference and an anomalous dark region; if the phase difference reached 360° (a full wavelength), it would produce complete constructive interference, creating an anomalous bright region.

Remember that magnification must always be a positive number. That's why we have taken the absolute value of y, which generally may be both positive and negative.

6. The second prism recombines the two rays into one polarised at 135°. The combination of the rays leads to interference, brightening or darkening the image at that point according to the optical path difference.

Focal lengthformulaforconvex lens

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The power (P) of a lens is the reciprocal of its focal length (f). Hence we can express the formula for the power of a lens as:

Differential interference contrast (DIC) microscopy, also known as Nomarski interference contrast (NIC) or Nomarski microscopy, is an optical microscopy technique used to enhance the contrast in unstained, transparent samples. DIC works on the principle of interferometry to gain information about the optical path length of the sample, to see otherwise invisible features. A relatively complex optical system produces an image with the object appearing black to white on a grey background. This image is similar to that obtained by phase contrast microscopy but without the bright diffraction halo. The technique was invented by Francis Hughes Smith.[1][citation needed] The "Smith DIK" was produced by Ernst Leitz Wetzlar in Germany and was difficult to manufacture. DIC was then developed further by Polish physicist Georges Nomarski in 1952.[2]

Focal lengthof convex lens

What isfocal lengthof lens

As explained above, the image is generated from two identical bright field images being overlaid slightly offset from each other (typically around 0.2 μm), and the subsequent interference due to phase difference converting changes in phase (and so optical path length) to a visible change in darkness. This interference may be either constructive or destructive, giving rise to the characteristic appearance of three dimensions.

No, the thin lens formula is not different for different lenses. The thin lens formula is the same for both convex and concave lenses.

One non-biological area where DIC is used is in the analysis of planar silicon semiconductor processing. The thin (typically 100–1000 nm) films in silicon processing are often mostly transparent to visible light (e.g., silicon dioxide, silicon nitride and polycrystalline silicon), and defects in them or contamination lying on top of them become more visible. This also enables the determination of whether a feature is a pit in the substrate material or a blob of foreign material on top. Etched crystalline features gain a particularly striking appearance under DIC.

2. The polarised light enters the first Nomarski-modified Wollaston prism and is separated into two rays polarised at 90° to each other, the sampling and reference rays.

Image quality, when used under suitable conditions, is outstanding[citation needed] in resolution. However analysis of DIC images must always take into account the orientation of the Wollaston prisms and the apparent lighting direction, as features parallel to this will not be visible. This is, however, easily overcome by simply rotating the sample and observing changes in the image.

The thin lens equation calculator will help you to analyze the optical properties of the simple lens. Keep reading to learn about the thin lens equation and understand how a lens can magnify the image of an object. Everything is about light, so be sure to check out the principles of light refraction too!

Equation for focal lengthcalculator

DIC works by separating a polarized light source into two orthogonally polarized mutually coherent parts which are spatially displaced (sheared) at the sample plane, and recombined before observation. The interference of the two parts at recombination is sensitive to their optical path difference (i.e. the product of refractive index and geometric path length). Adding an adjustable offset phase determining the interference at zero optical path difference in the sample, the contrast is proportional to the path length gradient along the shear direction, giving the appearance of a three-dimensional physical relief corresponding to the variation of optical density of the sample, emphasising lines and edges though not providing a topographically accurate image.

4. The rays travel through adjacent areas of the sample, separated by the shear. The separation is normally similar to the resolution of the microscope. They will experience different optical path lengths where the areas differ in refractive index or thickness. This causes a change in phase of one ray relative to the other due to the delay experienced by the wave in the more optically dense material.

Equation for focal lengthof lenses

If we place the object near the lens, we will get its image somewhere. The position, orientation, and size of this image depend on two things: the focal length of the lens (which is specific for the particular lens) and the position of the original object. We can predict what we will see with the following thin lens equation:

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Equation for focal lengthin physics

The image can be approximated (neglecting refraction and absorption due to the sample and the resolution limit of beam separation) as the differential of optical path length with respect to position across the sample along the shear, and so the differential of the refractive index (optical density) of the sample.

When sequentially shifted images are collated, the phase-shift introduced by the object can be decoupled from unwanted non-interferometric artifacts, which typically results in an improvement in contrast, especially in turbid samples.[3]

3. The two rays are focused by the condenser for passage through the sample. These two rays are focused so they will pass through two adjacent points in the sample, around 0.2 μm apart.

The image has the appearance of a three-dimensional object under very oblique illumination, causing strong light and dark shadows on the corresponding faces. The direction of apparent illumination is defined by the orientation of the Wollaston prisms.