Principle Construction, Working and Angular Magnification of Simple Microscope

Principle of Simple Microscope:

The principle of the simple microscope is based on the magnification of an image by using a simple convex lens.

Construction:

A simple microscope consists of one convergent lens only. The object is placed between the lens and its focal length, and the eye is placed just behind the lens. Then the eye sees a magnified, erect, and virtual image on the same side as the object at the least distance of distinct vision $(D)$ from the eye, and the image is then seen most distinctly.

Working:

If the small object $ab$ is placed between a lens $O$ and its first focus $f$ then Its magnified virtual image $a'b'$ is formed at a distance $D$ from the lens. Since the eye is just behind the lens, the distance of image $a'b'$ from the eye is also $D$.

Angular Magnification Or Magnifying Power($M$):

The ratio of the angle subtended by the image at the eye ($\beta$) to the angle subtended by the object at the eye when placed at the least distance of distinct vision ($\alpha$) is called the angular magnification or magnifying power.

$M= \frac{Angle \: subtended \: by \: the \: image \: at \: the \: eye \: (\beta)}{Angle \: subtended \: by \: the \: object \: at \: the \: eye \: when \\ placed \: at \: least \: distance \: of \: distinct \: vision \: (\alpha)}$

$M=\frac{\beta}{\alpha} \approx \frac{tan \beta}{tan \alpha} \quad (1)$

From figure

$tan \beta = \frac{ab}{oa} $

$tan \alpha = \frac{a_{1}b_{2}}{a_{1}o}$

Here $a_{1}b_{2} = ab$

$tan \alpha = \frac{ab}{a_{1}o}$

Now substitute these values in equation $(1)$, then

$M=\frac{\frac{ab}{ao}}{\frac{ab}{a_{1}o}}$

$M=\frac{a_{1}o}{ao}$

Here $ao = u$ (Distance between object and optical center of the lens) and $a_{1}o = D$ (Least Distance of distinct vision), then the above equation can be written as

$M=\frac{D}{u} \qquad(2)$

We know that the lens formula $\frac{1}{v}-\frac{1}{u} = \frac{1}{f}$

Now put
$v=-D$ (The image $a'b'$ is being formed at a distance $D$ from lens)
$u=-u$

$\frac{1}{-D}-\frac{1}{-u} = \frac{1}{f}$

Multiply $D$ in the above equation

$-\frac{D}{D}-\frac{D}{-u} = \frac{D}{f}$

$-1-\frac{D}{-u} = \frac{D}{f}$

$\frac{D}{u} =1 + \frac{D}{f} \qquad(3)$

From equation $(2)$ and equation $(3)$, then

$M=1 + \frac{D}{f} $

If eye is kept at distance $d$ from lens then $v=-(D-d)$, and the magnifying power will be

$M=1+\frac{D-d}{f}$

To see with a relaxed eye, the image $a'b'$ should be formed at infinity. In this case, the object $ab$ will be at the focus of the lens, i.e. $u=f$ then magnifying power

$M= \frac{D}{f} $

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Light and its properties

The basic definition of Light:

Light is a form of energy that produces the sensation of vision in the eye by which we can see objects.

There are some facts about light as follows:

1. Lightwave moves along a straight line path.

2. Light waves can travel through vacuum and medium both.

3. Light is an electromagnetic wave.

4. A light wave is the transverse wave in nature.

5. Light can be dispersed.

Besides these facts, light also shows the phenomenon of interference, diffraction, polarisation photoelectric effect, etc. To explain the above facts, many principles have been given from time to time, e.g., Newton's corpuscular theory, Huygen wave theory, Maxwell's principle of electromagnetic wave, Planck's quantum principle, dual nature of light, etc.

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Origin of Biomedical Signals

The biomedical signals differ from other signals only in terms of the application — signals that are used in the biomedical field. As such, biomedical signals are produced from a variety of sources. The following is a brief description of these sources:

1. Bioelectric signals: The bioelectric signal is unique to biomedical systems. It is produced by nerve cells and muscle cells. It is produced due to the membrane potential, which under certain conditions may be excited to generate an action potential. In single-cell measurements, the specific microelectrodes are used as sensors, and the action potential itself is considered as the biomedical signal. In more gross measurements, the surface electrodes are used as sensors, and the electric field generated by the action of many cells, distributed in the electrode’s vicinity, constitutes the bioelectric signal. Bioelectric signals are probably the foremost biosignals. The fact that most biosystems use excitable cells makes it possible, to use biosignals to study and monitor the main functions of the systems. The electric field propagates through the biological medium, and thus the potential may be acquired at relatively convenient locations on the surface, eliminating the need to invade the system. The bioelectric signal is acquired by a relatively simple transducer. A transducer is required in the field of biomedical because the electric conduction in the biomedical medium is executed through ions, while the conduction in the measurement system is executed through electrons. All these lead to the fact that the bioelectric signal is broadly used in most of the fields of biomedicine.

2. Bioimpedance signals: The impedance of the tissue contains important information related to its composition, blood volume, blood distribution, endocrine activity, autonomic nervous system activity, and many more. The bioimpedance signal is usually generated by injecting into the tissue under test sinusoidal currents (frequency range of $50 kHz–1 MHz$, with low current densities of the order of $20–20 mA$). The electrode polarization problems are minimized by choosing the frequency range and the low current densities are selected to prevent tissue damage mainly due to heating effects. Bioimpedance measurements are usually performed with four electrodes. Two electrodes (known as source electrodes) are used to inject the current into the tissue and these electrodes are connected to a current source. Remaining two electrodes (known as measuring electrodes) are placed on the tissue under investigation and used to measure the voltage drop generated by the current and the tissue impedance.

3. Bioacoustic signals: Many biomedical phenomena create acoustic noise. The measurement of this acoustic noise gives information about the underlying phenomenon. The flow of blood in the heart (i.e through the heart’s valves, or through blood vessels) generates typical acoustic noise. The flow of air through the upper and lower airways and in the lungs generates acoustic sounds. These sounds are called coughs, snores, and chest and lung sounds. These sounds are used extensively in medicine. Sounds are also produced in the digestive tract and in the joints. It also has been observed that the contracting muscle generates an acoustic noise or muscle noise. Since the acoustic energy propagates through the biological medium, the bioacoustic signal may be conveniently acquired on the surface, using acoustic transducers (microphones or accelerometers).

4. Biomagnetic signals: Many organs, such as the brain, heart, and lungs, produce extremely weak magnetic fields. The measurements of these fields provide information but are not included in other biosignals (such as bioelectric signals). Due to the low level of the magnetic fields to be measured, biomagnetic signals are usually of a very low signal-to-noise ratio. Extreme precautions must be taken in designing or developing the acquisition system of these signals.

5. Biomechanical signals: The term biomechanical signals includes all signals used in the biomedicine fields that originate from some mechanical function of the biological system. These signals include motion and displacement signals, pressure and tension signals, flow signals, and others. The measurement of bio-mechanical signals requires a variety of transducers, not always simple and inexpensive. The mechanical phenomenon does not propagate in biomedical signals, as do the electric, magnetic, and acoustic fields. Hence the measurement usually has to be performed at the exact site. This very frequently complex the measurement and forces it to be an invasive one.

6. Biochemical signals: The chemical measurements from the living tissue or from samples analyzed in the clinical laboratory produce biochemical signals. Measuring the concentration of various ions inside and around a cell using specific ion electrodes. It is an example of such a signal. Partial pressures of oxygen (pO2) and carbon dioxide (pCO2) in the blood or respiratory system are other examples. Biochemical signals are often very low-frequency signals. Mostly, biochemical signals are actually DC signals.

7. Biooptical signals: Bio-optical signals are the result of optical functions of the biological system, occurring naturally or induced by the measurement. Blood oxygenation may be analyzed by measuring the transmitted and backscattered light from a tissue ( i.e.in vivo and in vitro) in several wavelengths. Important information about the fetus may be acquired by measuring the fluorescence characteristics of the amniotic fluid. Analysis of the Heart output may be performed by the dye dilution method, which requires the observation of the appearance of recirculated dye in the bloodstream. The development of fiberoptic technology has opened vast applications of bio-optical signals.

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