Magnifying power of the microscope. Image quality. Device resolution

Goal of the work. Familiarization with the device of a microscope and determination of its resolution.

Devices and accessories: Microscope, metal plate with a small hole, lighting mirror, ruler with scale.

Introduction

A microscope consists of a lens and an eyepiece, which are complex lens systems. The path of rays in a microscope is shown in Fig. 1, in which the objective and eyepiece are represented by single lenses.

The object in question AB is placed a little further from the main focus of the lens F about. The microscope lens gives a real, inverse and magnified image of the object (AB in Fig. 1), which is formed behind the double focal length of the lens. The magnified image is viewed by the eyepiece as a magnifying glass. The image of an object viewed through the eyepiece is virtual, inverse and enlarged.

The distance between the back focus of the lens and the front focus of the eyepiece is called optical spacing of the system or optical tube length microscope .

The magnification of a microscope can be determined by the magnification of the objective and eyepiece:

N = N about  N about = ───── (1)

f about  f ok

where N about and N about are the magnification of the lens and eyepiece, respectively; D - distance of best vision for a normal eye (~25 cm);  is the optical length of the microscope tube; f about and f OK- main focal lengths of the lens and eyepiece.

When analyzing formula (1), we can conclude that microscopes with high magnification can examine any small objects. However, the useful magnification provided by a microscope is limited by diffraction phenomena, which become noticeable when viewing objects whose dimensions are comparable to the wavelength of light.

Resolution limit microscope is the smallest distance between points, the image of which is obtained separately in the microscope.

According to Abbe's theory, the resolution limit of a microscope is determined by the expression:

d = ───── (2)

where d is the linear size of the object in question;  - wavelength of the light used; n is the refractive index of the medium between the object and the lens;  is the angle between the main optical axis of the microscope and the boundary ray (Fig. 2).

IN the quantity A = nsin is called numerical aperture of the lens , and the reciprocal of d is microscope resolution . From expression (2) it follows that the resolution of the microscope depends on the numerical aperture of the lens and the wavelength of light that illuminates the object in question.

If the object is in the air (n=1), then in the microscope it is possible to distinguish points of the object, the distance between which is:

d = ─────

For microscopic objects, the angle  is close to 90 degrees, then sin  1, which means that objects located at a distance of ~ 0.61 from each other can be examined in a microscope. In the case of visual observations (the maximum sensitivity of the eye falls on the green region of the visible spectrum   550 nm), objects located at a distance of ~300 nm can be seen in a microscope.

As follows from expression (2), the resolution of a microscope can be increased by reducing the wavelength of light that illuminates the object. Thus, when photographing objects in ultraviolet light (~ 250-300 nm), the resolution of the microscope can be doubled.

Item h placed slightly further than the front focus of the lens. The lens gives real, inverse, augmented image H’ , located between the front focus of the eyepiece and the optical center of the eyepiece. This intermediate image is viewed through the eyepiece as if through a magnifying glass. The eyepiece gives imaginary, direct, magnified image H, which is located at the distance of best vision S ≈ 25 cm from the optical center of the eye.

We look at this image with our eyes and it forms on its retina. real, inverse, reduced image.

Microscope Magnification– the ratio of the dimensions of the virtual image to the dimensions of the object viewed through the microscope:
. Multiply the numerator and denominator by the size of the intermediate image H’ :
. Thus, the magnification of the microscope is equal to the product of the objective magnification and the eyepiece magnification. Lens magnification can be expressed in terms of the characteristics of the microscope using the similarity of right triangles
, Where Loptical tube length: the distance between the back focus of the lens and the front focus of the eyepiece (we assume that L >> F about). Eyepiece magnification
. Therefore, the magnification of the microscope is:
.

4. Resolution and resolution limit of the microscope. Diffraction phenomena in a microscope, the concept of Abbe's theory.

Microscope resolution limitz - this is the smallest distance between two points of an object viewed through a microscope, when these points are still perceived separately. The resolution limit of a conventional biological microscope lies in the range of 3-4 microns. Resolution microscope is the ability to provide a separate image of two closely located points of the object under study, that is, this is the reciprocal of the resolution limit.

Diffraction of light places a limit on the ability to distinguish the details of objects when they are observed through a microscope. Since light does not propagate rectilinearly, but bends around obstacles (in this case, the objects in question), images of small details of objects turn out blurry.

E. Abbe suggested diffraction theory of microscope resolution. Let the object that we want to examine through a microscope be a diffraction grating with a period d. Then the minimum detail of the object that we must distinguish will be precisely the lattice period. Light diffraction occurs on the grating, but the diameter of the microscope objective is limited, and at large diffraction angles, not all the light passing through the grating enters the objective. In reality, light from an object propagates towards the lens in a certain cone. The resulting image is closer to the original, the more maxima involved in the formation of the image. Light from an object propagates to the lens from a condenser in the form of a cone, which is characterized by angular aperture u- the angle at which the lens is visible from the center of the object under consideration, that is, the angle between the outer rays of the conical light beam entering the optical system. According to E. Abbe, to obtain an image of a grating, even the most fuzzy one, rays of any two orders of the diffraction pattern must enter the lens, for example, rays forming the central and at least the first diffraction maximum. Let us recall that for the oblique incidence of rays on a diffraction grating, its main formula has the form: . If the light comes at an angle , and the diffraction angle for first maximum equals
, then the formula takes the form
. The resolution limit of the microscope should be taken as the constant of the diffraction grating, then
, where  is the wavelength of light.

As can be seen from the formula, one way to reduce the resolution limit of a microscope is to use light with a shorter wavelength. In this regard, an ultraviolet microscope is used, in which microobjects are examined in ultraviolet rays. The basic optical design of such a microscope is similar to that of a conventional microscope. The main difference is the use of optical devices that are transparent to UV light and the image registration features. Since the eye does not perceive ultraviolet radiation (in addition, it burns the eyes, i.e. is dangerous for the organ of vision), photographic plates, fluorescent screens or electro-optical converters are used.

If a special liquid medium called immersion, then the resolution limit also decreases:
, Where n– absolute refractive index of immersion, A – lens numerical aperture. Water is used as immersion ( n = 1.33), cedar oil ( n= 1.515), monobromonaphthalene ( n = 1.66), etc. For each type of immersion, a special lens is made, and it can only be used with this type of immersion.

Another way to reduce the resolution limit of a microscope is to increase the aperture angle. This angle depends on the size of the lens and the distance from the subject to the lens. However, the distance from the object to the lens cannot be changed arbitrarily; it is constant for each lens and the object cannot be brought closer. In modern microscopes, the aperture angle reaches 140 o (respectively, u/2 = 70 o). With this angle, maximum numerical apertures and minimum resolution limits are obtained.

The data is given for an oblique incidence of light on an object and a wavelength of 555 nm, to which the human eye is most sensitive.

Please note that the eyepiece does not affect the resolution of the microscope at all, it only creates a magnified image of the lens.

where l is the distance between the upper focus of the lens and the lower focus of the eyepiece; L – distance of best vision; equal to 25 cm; F 1 and F 2 – focal lengths of the lens and eyepiece.

Knowing the focal lengths F 1, F 2 and the distance between them l, you can find the magnification of the microscope.

In practice, microscopes with magnifications greater than 1500–2000 are not used, because The ability to distinguish small details of an object in a microscope is limited. This limitation is caused by the influence of light diffraction in the passing structure of a given object. In this regard, the concepts of resolution limit and resolving power of a microscope are used.

Determining the limit of microscope resolution

Microscope resolution limit is the smallest distance between two points on an object at which they are visible separately in a microscope. This distance is determined by the formula:

,

where λ is the wavelength of light; n is the refractive index of the medium between the lens and the object; u is the aperture angle of the lens, equal to the angle between the outer rays of the conical light beam entering the microscope lens.

In reality, light from an object propagates to the microscope lens in a certain cone (Fig. 2 a), which is characterized by an angular aperture - the angle u between the outer rays of a conical light beam entering the optical system. In the limiting case, according to Abbe, the outer rays of the conical light beam will be the rays corresponding to the central (zero) and 1st main maxima (Fig. 2 b).

The quantity 2nsin U is called the numerical aperture of the microscope. The numerical aperture can be increased using a special liquid medium - immersion– in the space between the objective and the cover glass of the microscope.

In immersion systems, compared to identical “dry” systems, a larger aperture angle is obtained (Fig. 3).

Fig.3. Immersion system diagram

Water (n = 1.33), cedar oil (n = 1.514), etc. are used as immersion. For each immersion, a lens is specially calculated, and it can only be used with this immersion.

The formula shows that the resolution limit of the microscope depends on the wavelength of light and the numerical aperture of the microscope. The shorter the wavelength of light and the larger the aperture, the smaller Z, and, therefore, the greater the resolution limit of the microscope. For white (daylight) light, the average wavelength can be taken as λ = 0.55 µm. The refractive index for air is n = 1.

Microscope mbs-1

MBS-1 is a stereoscopic microscope that provides a direct three-dimensional image of the object under consideration in both transmitted and reflected light.

The microscope consists of 4 main parts:

– table;

– tripod;

– optical head with a coarse feed mechanism;

– eyepiece attachment.

The microscope stage consists of a round body, inside of which a rotating reflector with mirror and matte surfaces is mounted. To work with daylight, the housing has a cutout through which light passes freely. On the back side of the table body there is a threaded hole for working with an electric illuminator. An optical head is attached to the microscope stand - the main part of the device, into which the most important optical components are mounted.

The housing of the optical head contains a drum with Galilean systems installed in it. Rotate the drum axis using handles with printed numbers 0.6; 1; 2; 4; 7 achieve different lens magnifications. Each position of the drum is clearly fixed with a special spring clamp. Using the handle on the microscope tripod, which moves the optical head, the sharpest image of the object in question is achieved.

The entire optical head can be moved on the tripod rod and secured in any position with a screw. The eyepiece attachment consists of a guide, which is a rectangular piece with two holes for lens frames.

When observing through the eyepieces, you need to turn the eyepiece tubes to find a position in which the two images are combined into one. Next, focus the microscope on the object under study, and rotate the reflector to achieve uniform illumination of the field. When adjusting the illumination, the socket with the lamp moves towards the collector until the best illumination of the observed object is obtained.

Basically, MBS-1 is intended for preparation work, for observing objects, as well as for carrying out linear measurements or measuring the areas of sections of the preparation. The optical diagram of the microscope is shown in Fig. 4.

The optical diagram of the MBS-1 microscope is shown in Fig. 4.

When working in transmitted light, the light source (1) with the help of a reflector (2) and a collector (3) illuminates a transparent specimen mounted on the stage (4).

A special system was used as a lens, consisting of 4 lenses (5) with a focal length = 80 mm and 2 pairs of Galilean systems (6) and (7), behind which there are lenses (8) with a focal length of 160 mm, which form an image of the object in the focal planes of the eyepieces.

The total linear magnification of the optical system, consisting of a lens (5), Galilean systems (6) and (7) and lenses (8) is: 0.6; 1; 2; 4; 7. Behind the lenses (8) there are 2 Schmidt prisms (9), which allow you to rotate the eyepiece tubes according to the observer’s eye without rotating the lens image.

1 – light source;

2 – reflector;

3 – collector;

4 – object table;

5 – lens (F = 80 mm);

6, 7 – Galilean systems;

8 – lenses (F = 160 mm);

9 – Schmidt prisms;

10 – eyepieces.

Rice. 4. Optical design of the MBS-1 microscope

The MBS-1 microscope comes with 3 pairs of eyepieces (10) with a magnification of 6; 8; 12.5 and one 8x magnification eyepiece micrometer with reticle. They allow you to vary the overall magnification of the microscope from 3.6 to 88 (Table 1). The total magnification of a microscope is the product of the magnification of the eyepiece and the magnification of the objective.

Table 1.

Optical characteristics of the MBS-1 microscope

Increase

Lens magnification

The resolution of the eye is limited. Resolution characterized resolved distance, i.e. the minimum distance between two neighboring particles at which they are still visible separately. The resolved distance for the naked eye is about 0.2 mm. A microscope is used to increase resolution. To study the structure of metals, the microscope was first used in 1831 by P.P. Anosov, who studied damask steel, and later, in 1863, by the Englishman G. Sorby, who studied meteorite iron.

The permitted distance is determined by the relationship:

Where l- wavelength of light coming from the object of study to the lens, n– refractive index of the medium located between the object and the lens, and a- angular aperture equal to half the opening angle of the beam of rays entering the lens that produces the image. This important characteristic of the lens is engraved on the lens frame.

Good lenses have a maximum aperture angle a = 70° and sina » 0.94. Most studies use dry objectives operating in air (n = 1). To reduce the resolved distance, immersion lenses are used. The space between the object and the lens is filled with a transparent liquid (immersion) with a high refractive index. Typically a drop of cedar oil is used (n = 1.51).

If we take l = 0.55 µm for visible white light, then the minimum resolving distance of a light microscope is:

Thus, the resolving power of a light microscope is limited by the wavelength of light. The lens magnifies the intermediate image of the object, which is viewed through the eyepiece, as if through a magnifying glass. The eyepiece magnifies the intermediate image of the object and cannot increase the resolution of the microscope.

The total magnification of the microscope is equal to the product of the magnification of the objective and the eyepiece. Metallographic microscopes are used to study the structure of metals with magnification from 20 to 2000 times.

Beginners make a common mistake by trying to view the structure immediately at high magnification. It should be kept in mind that the greater the magnification of an object, the smaller the area visible in the field of view of the microscope. Therefore, it is recommended to begin the study by using a weak lens in order to first assess the general nature of the metal structure over a large area. If you start microanalysis using a strong lens, then many important features of the metal structure may not be noticed.

After a general view of the structure at low magnifications of the microscope, a lens with such a resolution is selected to see all the necessary smallest details of the structure.

The eyepiece is chosen so that the details of the structure, magnified by the lens, are clearly visible. If the eyepiece magnification is not sufficient, the fine details of the intermediate image created by the lens will not be seen through the microscope, and thus the full resolution of the lens will not be used. If the eyepiece magnification is too high, new structural details will not be revealed, at the same time, the contours of already identified details will be blurred, and the field of view will become narrower. The eyepiece's own magnification is engraved on its frame (for example, 7 x).



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