Magnificationformula Biology

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 Figure 2.26). Thus, when such an image produced by a convex lens serves as the object for the eye, as shown in Figure 2.37, 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.

We will explore different typesof laser, their features, and how they are used in various applications. Join us for a fascinating look at the world of lasers and their multifaceted role in modern.

When selecting a laser, it’s crucial to consider factors such as the desired precision, power requirements, material sensitivity, and the specific application needs. Each type of laser offers unique advantages, making the choice highly dependent on the intended use case.

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By comparing Equation 2.29 with Equation 2.32, we see that the range of angular magnification of a given converging lens is

Femtosecond lasers are ultrashort pulsed lasers with pulse widths in the femtosecond range (10^-15 seconds). They are known for their ultra-short pulse width and high peak power.

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The apparent size of an object perceived by the eye depends on the angle the object subtends from the eye. As shown in Figure 2.36, 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′OA′) than when it is positioned at B (see OB′OB′). Thus, objects that subtend large angles from the eye appear larger because they form larger images on the retina.

A laser is a device that emits a focused and coherent beam of light through stimulated emission, consisting of a gain medium (gas, liquid, solid, or semiconductor) that amplifies light, an energy source (pump) that excites the atoms, and an optical cavity with mirrors that intensify the light to form a laser beam. Lasers are known for their precision and are widely used in fields like manufacturing and medicine.

Versatile Applications: Used extensively in material processing (cutting, welding), medical devices (therapeutic instruments), scientific research (spectroscopy), and industrial measurements.

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 2.37. 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 θimageθimage subtended by the image to the angle θobjectθobject subtended by the object:

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Application: UV lasers are used in electronics, medicine, and materials science for different purposes. They are used for processing integrated circuit boards, treating skin and tumors, and processing micro-optical components. They are also utilized in the semiconductor industry for micromachining and solar panel development.

Application: Solid-state lasers are suitable for a wide range of applications, including industrial processing (cutting, welding, marking), medical procedures (eye surgery, tumor treatment), scientific research (spectroscopy, nonlinear optics), and military applications (laser guidance, target indication).

Lasers have revolutionized various industries with their precision, efficiency, and versatility. From fiber lasers known for their high efficiency and compact size to femtosecond lasers prized for ultra-short pulses and precision processing, each type of laser brings unique advantages to the table. Whether it’s for industrial cutting and welding, medical surgeries, scientific research, or military applications, there’s a laser solution tailored to meet specific needs.

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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)(ℓ=0), then L=di=25cmL=di=25cm and Equation 2.27 becomes

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How to find magnificationequation

Application: Gas lasers are widely used in industrial processing (cutting, welding, marking), medical treatments (dermatology, ophthalmology), scientific research (spectroscopy, photochemistry), and commercial applications (laser printers, hologram production).

How to find magnificationof a lens

It is also used in performing eye surgery, such as LASIK. Additionally, lasers are used for precise cutting and micromachining in industries. They also have potential applications in military and security for LIDAR and target tracking.

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 (L=25cmL=25cm) to get maximum magnification, and we hold the magnifying lens close to the eye (ℓ=0ℓ=0). In this case, Equation 2.29 gives

Lasers are versatile tools that can be broadly categorized based on their output characteristics into continuous wave (CW) lasers and pulsed lasers. Each type has unique operational principles and application areas, making them suitable for different tasks.

From part (b) of the figure, we see that the absolute value of the image distance is |di|=L−ℓ|di|=L−ℓ. Note that di<0di<0 because the image is virtual, so we can dispense with the absolute value by explicitly inserting the minus sign: −di=L−ℓ−di=L−ℓ. Inserting this into Equation 2.28 gives us the final equation for the angular magnification of a magnifying lens:

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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.

Application: Fiber lasers are ideal for industrial applications such as metal cutting, welding, and marking. They are used in medical procedures, communication systems, and military applications for laser guidance and countermeasures. They are also used in eye surgery and tumor treatment.

Gas lasers operate through excited emission from a gas discharge and are known for their good monochromaticity and coherence.

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UV lasers are capable of generating light in the ultraviolet wavelength band and are known for their high coherence, efficiency, and precision.

Consider the situation shown in Figure 2.37. The magnifying lens is held a distance ℓℓ 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 ℓℓ. In the small-angle approximation, the angular size θimageθimage of the image is hi/Lhi/L. The angular size θobjectθobject of the object at the near point is θobject=ho/25cmθobject=ho/25cm. The angular magnification is then

Magnificationformula for mirror

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Pulsed lasers emit laser light in short bursts or pulses. They can achieve high peak power in very brief periods, making them suitable for applications requiring high energy but minimal thermal impact.

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Solid-state lasers use crystals or glass doped with rare earth elements as the gain medium. They are favored for their stability, high beam quality, and efficiency.

Diverse Applications: Employed in various fields like ophthalmic surgery, laser marking, scientific research (time-resolved spectroscopy), military, and industrial processing.

Fiber lasers use optical fibers with rare earth elements like erbium, ytterbium, and neodymium as the gain medium. They are known for their high efficiency, compact size, and excellent beam quality.

where m is the linear magnification (Equation 2.32) derived for spherical mirrors and thin lenses. Another useful situation is when the image is at infinity (L=∞)(L=∞). Equation 2.29 then takes the form

Use Cases: Femtosecond lasers are used in scientific research for studying ultrafast phenomena and time-resolved spectroscopy. Laser technology is important for various applications. It is used in making electronics and nanotechnology materials.

Continuous wave lasers emit a constant, uninterrupted laser beam. They are known for their stable output and are ideal for applications requiring prolonged laser exposure.