Thanks to its low refractive index, CaF2 windows are also ideal for high-precision applications, such as microscopes and telescopes.

By comparing Equations \ref{eq13} and \ref{eq15}, we see that the range of angular magnification of a given converging lens is

Magnifying glassuses

We need to determine the requisite magnification of the magnifier. Because the jeweler holds the magnifying lens close to his eye, we can use Equation \ref{eq13} to find the focal length of the magnifying lens.

which shows that the greatest magnification occurs for the lens with the shortest focal length. In addition, when the image is at the near-point distance and the lens is held close to the eye (\(ℓ=0\)), then \(L=d_i=25\,cm\) and Equation \ref{eq12} becomes

We supply premium-quality calcium fluoride optical lenses for various applications, including vacuum ultraviolet (VUV) and infrared (IR) spectroscopy, semiconductor lithography, thermal imaging devices and excimer lasers.

Low absorption: Calcium fluoride has a low absorption coefficient, and therefore can transmit light with minimal loss. This property makes it useful for optical components in high-power laser systems.

From Figure \(\PageIndex{1b}\), we see that the absolute value of the image distance is \(|d_i|=L−ℓ\). Note that \(d_i<0\) because the image is virtual, so we can dispense with the absolute value by explicitly inserting the minus sign:

What's a magnifying glassfor reading

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a. The required linear magnification is the ratio of the desired image diameter to the diamond’s actual diameter (Equation \ref{eq15}). Because the jeweler holds the magnifying lens close to his eye and the image forms at his near point, the linear magnification is the same as the angular magnification, so

Inserting Equation \ref{eq34} into Equation \ref{eq10} gives us the final equation for the angular magnification of a magnifying lens:

Magnifyinglens concave or convex

Note that a greater magnification is achieved by using a lens with a smaller focal length. We thus need to use a lens with radii of curvature that are less than a few centimeters and hold it very close to our eye. This is not very convenient. A compound microscope, explored in the following section, can overcome this drawback.

Note that all the quantities in this equation have to be expressed in centimeters. Often, we want the image to be at the near-point distance (e.g., \(L=25\,cm\)) to get maximum magnification, and we hold the magnifying lens close to the eye (\(ℓ=0\)). In this case, Equation \ref{eq12} gives

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10 uses ofmagnifying glass

High resistance to radiation damage: Calcium fluoride is highly resistant to radiation damage, making it useful in applications that involve radiation exposure.

Low dispersion: Calcium fluoride has a low dispersion, meaning that it can transmit light of different wavelengths without significant colour separation or distortion.

We have seen that, when an object is placed within a focal length of a convex lens, its image is virtual, upright, and larger than the object (see part (b) of this Figure). Thus, when such an image produced by a convex lens serves as the object for the eye, as shown in Figure \(\PageIndex{2}\), the image on the retina is enlarged, because the image produced by the lens subtends a larger angle in the eye than does the object. A convex lens used for this purpose is called a magnifying glass or a simple magnifier.

What's a magnifying glassvsmagnifying glass

Our mirrors made from calcium fluoride have been used in various laser and industrial machinery, including excimer lasers, free-space lasers and cryogenically cooled thermal imaging systems.

Calcium fluoride (CaF2) is a crystalline compound with a cubic crystal structure. This popular optical material can be used across a wide range of ultraviolet (UV), visible, or infrared (IR) applications due to its unique optical properties.

High thermal stability: Calcium fluoride has a high thermal stability, allowing it to be used in high-temperature applications without significant degradation of its optical properties.

High damage threshold and mechanical strength: The mechanical properties of calcium fluoride include an impressive ultimate tensile strength (UTS) of 34.1 to 157 MPa. CaF2 also offers excellent water, chemical, and heat resistance.

where \(m\) is the linear magnification (Equation \ref{mag}) previously derived for spherical mirrors and thin lenses. Another useful situation is when the image is at infinity (\(L=\infty\)). Equation \ref{eq12} then takes the form

At Global Optics, our CaF2 prisms can be used for wavelength separation and image rotation applications, and IR and UV optics.

How doesa magnifying glasswork

Consider the situation shown in Figure \(\PageIndex{1b}\). The magnifying lens is held a distance \(ℓ\) from the eye, and the image produced by the magnifier forms a distance \(L\) from the eye. We want to calculate the angular magnification for any arbitrary \(L\) and \(ℓ\). In the small-angle approximation, the angular size \(θ_{image}\) of the image is \(h_i/L\). The angular size \(θ_{object}\) of the object at the near point is \(θ_{object}=h_o/25\,cm\). The angular magnification is then

To account for the magnification of a magnifying lens, we compare the angle subtended by the image (created by the lens) with the angle subtended by the object (viewed with no lens), as shown in Figure \(\PageIndex{1a}\). We assume that the object is situated at the near point of the eye, because this is the object distance at which the unaided eye can form the largest image on the retina. We will compare the magnified images created by a lens with this maximum image size for the unaided eye. The magnification of an image when observed by the eye is the angular magnification \(M\), which is defined by the ratio of the angle \(θ_{image}\) subtended by the image to the angle \(θ_{object}\) subtended by the object:

High transmittance: Calcium fluoride has a high transmittance across a wide range of wavelengths, making it a useful material for applications in ultraviolet, visible, and infrared regions of the electromagnetic spectrum.

What's a magnifying glassused for

Given that calcium fluoride's optical properties are so adaptable across a broad spectrum, many industries can benefit from CaF2 components.

The apparent size of an object perceived by the eye depends on the angle the object subtends from the eye. As shown in Figure \(\PageIndex{1}\), the object at \(A\) subtends a larger angle from the eye than when it is position at point \(B\). Thus, the object at \(A\) forms a larger image on the retina (see \(OA′\)) than when it is positioned at \(B\) (see \(OB′\)). Thus, objects that subtend large angles from the eye appear larger because they form larger images on the retina.

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Overall, the combination of high transmittance, low absorption, low dispersion, and high thermal stability makes calcium fluoride a useful material for a variety of optical applications.

10 uses ofmagnifying glassin laboratory

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\[\underbrace{ M=\dfrac{θ_{image}}{θ_{object}}=\dfrac{h_i(25cm)}{Lh_o}}_{\text{angular magnification}} . \label{angular magnification} \]

Low refractive index: Calcium fluoride has a relatively low refractive index of 1.43 or homogeneity, making it useful for optical components such as lenses and prisms.

b. To get an image magnified by a factor of ten, we again solve Equation \ref{eq13} for \(f\), but this time we use \(M=10\). The result is

The resulting magnification is simply the ratio of the near-point distance to the focal length of the magnifying lens, so a lens with a shorter focal length gives a stronger magnification. Although this magnification is smaller by 1 than the magnification obtained with the image at the near point, it provides for the most comfortable viewing conditions, because the eye is relaxed when viewing a distant object.

Here at Global Optics, we're experienced and trusted suppliers of calcium fluoride optics, from lenses and windows to prisms and other optical components.

Our calcium fluoride optical windows are ideal for spectroscopy applications, UV laser systems and fluorescence imaging, offering excellent performance, as well as water and fogging resistance.

A jeweler wishes to inspect a 3.0-mm-diameter diamond with a magnifier. The diamond is held at the jeweler’s near point (25 cm), and the jeweler holds the magnifying lens close to his eye.

\[\begin{align} M&= \left(−\dfrac{d_i}{d_o}\right)\left(\dfrac{25\,cm}{L}\right) \\[4pt] &=−d_i\left(\dfrac{1}{f}−\dfrac{1}{d_i}\right)\left(\dfrac{25\,cm}{L}\right) \\[4pt] &= \left(1−\dfrac{d_i}{f}\right)\left(\dfrac{25\,cm}{L}\right) \label{eq10} \end{align} \]