Microscopes - simple and compound

Optical Instruments

An optical instrument is a device which is constructed by a suitable combination of mirrors, prisms and lenses. The principle of working of an optical instrument is based on the laws of reflection and refraction of light. 

     The common types of optical instruments are :

     (i) Projection instruments. These are used to project on the screen a real, inverted and magnified image of an opaque or transparent object so as to be viewed by a large audience. The object is, however, so fitted that its image is seen in erect form. 

     An eye, a photographic camera, a projection lantern, an episcope, an epidiascope, an overhead projector, a film projector, etc. are examples of projection instruments. 

    (ii) Microscopes. These are used to see very small objects in magnified form which otherwise cannot be seen distinctly when placed close to the necked eye.

  

     Examples : a simple microscope and compound microscope. 

   (iii) Telescopes. These are used to see astronomical and distant objects in magnified form which otherwise cannot be seen clearly with the necked eye. 

     Examples : an astronomical telescope, a Galilean telescope, a terrestrial telescope, a reflecting telescope, etc. 

Simple magnifier - "Simple Microscope"

     Principle. When an object is placed between a convex lens and its principal focus, an erect, virtual and magnified image is formed on the same side as the object. A single convex lens, of short focal length thus used constitutes a simple microscope which is commonly known as a magnifying glass or a reading glass. 

     Formation of image. A convex lens is then interposed between the eye and the object so that the distance 'μ' of the object from the lens is less than the focal length 'f' of the lens. A virtual, erect and magnified image A'B' will be produced. By adjusting 'u', the image is set at least distance of distinct vision (D = 25 cm) from the eye so that the image becomes most district. The rays of light forming the virtual and magnified image A'B' of the small object AB as seen through the lens by placing the eye very close to it are shown in Fig. 1. 

Fig. 1. Simple microscope. 

Magnifying power of magnification

     Case (i) When the image is obtained at the distance of district vision from eye

     The magnifying power of a simple microscope is defined as the ratio between the angle subtended by the image at the eye to the angle subtended by the object at the eye when both the image and the object are situated at the distance of distinct vision. 

     Thus, if θi is the angle which the image A'B' subtends at the eye and θ0 is the angle which the object AB (= CB') subtends at the eye when both are placed at the least distance of distinct vision D, then 

     Magnifying power, 

   

     M = θi/θ0 = tan θi/tan θ0    (∵   ㄥs are small) 

        

         = (AB/OB)/(CB'/OB') 

      

        = AB/OB × OB'/CB'

        = OB'/OB                        (∵   AB = CB') 

        = -D/-u = D/u                                    ... (1) 

     Since the virtual image A'B' is formed at the least distance of distinct vision from the lens, therefore, v = -D. 

     Using lens formula, 1/v - 1/u = 1/f

               Distance of object = -u

               Distance of image = -D

     ∴     -1/D + D/u = D/f     or     -1 + D/u = D/f

     Multiplying both sides by D, we get 

     - D/D + D/u = D/f    or    -1 + D/u = D/f

       D/u = 1 + D/f                                     ... (2) 

     From equation (1) and (2), we get

               M = 1 + D/f

     Thus, a convex lens of shorter focal length yields higher magnification. 

     Case (ii) When the final image is formed at infinity

     When the image is formed at infinity, the rays enter the eye as parallel beam. So, the eyes does not have to exert any accommodation power and is in the relaxed position. 

     Magnifying power of simple microscope in such a case is given by the ratio between the angle subtended at the eye by the image (at infinity) to that subtended by the object when placed at distance of distinct vision. 

     Ray diagram is shown in Fig. 2. The object shall have to be at principal focus  so as to obtain image at infinity. 

Fig. 2. Image at infinity. 

     Here         M = θi/θ0

or        M = (AB/BO)/(CB'/OB')      [∵  CB' = AB]

     ∴     M = D/f                                        ... (3) 

     On comparing equations (2) and (3) we find that the magnifying power of the simple microscope is slightly smaller than that in first case. But in second case there is no strain on eye because of no accommodation power 

Uses. A simple microscope is used by :

     (i) astrologers to read fate-lines of the hand, 

    (ii) biology students to see the slides, 

   (iii) watch repairers to locate defects, 

  

   (iv) detective department to match finger prints. 

Compound Microscope

The magnification produced by a simple microscope is generally not sufficient to give a detailed view of two very closely situated objects. A combination of two convex lenses is employed to have a large magnification. The instrument so designed is known as a compound microscope. 

  

     The convex lens O of short focal length and small aperture, which faces the object to be viewed is known as the objective. The convex lens E of small focal length and comparatively large aperture near the eye is known as eye piece. 

     The two lenses are placed in two metal tube so as to have a common principal axis. The eye piece is fitted in a draw tube and can be slided within the main tube by means of rack and pinion arrangement to focus the microscope upon the object. 

     Let AB be an extended object situated on the principal axis at a distance slightly greater than the focal length of the objective. As refraction takes place through the objective O, a real, inverted and magnified image A₁B₁ is formed. 

     The lens E is so adjusted that A₁B₁ falls within its focal length and so the final virtual image A₂B₂ of A₁B₁ is obtained at the distance of distinct vision 'D' from the eye. The final image A₂B₂ is thus, highly magnified but is inverted with respect to the object AB. The course of ray forming the final image is shown in Fig. 3.

Fig. 3. Compound microscope. 

Magnifying power or magnification

     Case (i) when the final image is obtained at the distance of distinct vision from the eye

     The magnifying power of a compound microscope is defined as the angle subtended by the final image at the eye to the angle subtended by the object at the eye when both the object and the image are situated at the distance of distinct vision from the eye. 

     If the object was situated at B₂, it would have occupied length B₂C such that

 

                   B₂C = AB

     Let the angles subtended by the object B₂C and final image A₂B₂ at the eye be θi and θ0 respectively. 

     The magnification M of the microscope is, then given by, 

             M = θi/θ0 = tan θi/tan θ0

                          (∵ ㄥs θi and θ0 are very small) 

     In triangle O₂B₂C, 

               tan θ0 = B₂C/O₂B₂

     In triangle O₂B₂A₂, 

   

              tan θi = A₂B₂/O₂B₂

               M = A₂B₂/AB 

    

                   = (A₂B₂/A₁B₁) × (A₁B₁/AB) 

     But      A₁B₁/AB = M₁ and A₂B₂/A₁B₁ = M₂

where M₁ and M₂ are magnifications produced by the two lenses Of and E respectively. 

     ∴            M = M₁ × M₂                            ... (4) 

     For the lens O, M₁ = v/u

               v = distance of image

               u = distance of object

     Again, since the lens E acts like a simple microscope, its magnification M₂ is given by

                 M₂ = 1 + (D/fe) 

where fe is the focal length of the eye piece. Substituting for M₁ and M₂ in equation (4), we get

                M = v/u (D/fe)                            ... (5) 

     If the object AB is situated very near the principal focus of the objective, the image A₁B₁ will be far removed from the lens O. 

     In that case,

       

           u = fo= focal length of the objective

           v = L = length of the microscope tube

    ∴        M = L/fo (D/fe)                               ... (6) 

     It is clear from equation (5) that in order to have a microscope of large magnification, the two lenses used should have small focal lengths. 

     A good microscope has magnification as high as 2000 or even more. 

    Case (ii) when the final image is obtained at infinity

     Ray diagram for such a case in shown in Fig. 4. 

     Magnifying power M₁ produced by the object is same as discussed above. 

             M₁ = v/u = L/fo

  

     Magnifying power M₂ of the eye piece (acting as a simple microscope set for final image at infinity) is given by equation (3) 

              M₂ = D/fe

Fig. 4. Final image at infinity. 

     Therefore, net magnifying power of the compound microscope is given by

               M = M₁ × M₂

or          M = L/fo × D/fe                             ... (7) 

Resolving power of an optical instrument

Angle subtended by two objects at the eye depends upon the separation between them and at their distances from eye 

     The angle may be small in two cases :

     (i) When the two objects are situated very close to each other. 

    (ii) When the two objects (may be widely separated) are situated at large distance away, e.g., stars etc. 

     It is a limitation of human eye that if this angle is less than one minute, the two objects cannot be distinguished as separate. Therefore, in order to see objects as separate, we may use of optical instruments. A lens system (telescope or microscope) is used to resolve two points-objects, while prism and grating are used to resolve two very closely situated spectral lines. 

     The process of separation of such closely situated objects is called resolution and the ability of an optical instrument to produce their image as distinctly separate is called the resolving power. 

Or

     The resolving power of an optical instrument is defined as the ability of the instrument to see two objects as just separate. 

     Resolving power is measured by the minimum distance (∆x) between two objects which just appear as separate through the instrument. Smaller the value of ∆x, greater is the resolving power of the instruments and vice-versa. 

Resolving power of a microscope

Let d be the minimum distance between two objects which can just be distinguished as separate. This distance is called resolving limit of the instrument and is a measure of the resolving power of the instrument. 

Fig. 5. Objective of a microscope. 

     Smaller in value of resolving limit, greater is the resolving power of the instrument. 

Microscope

For a microscope

               d = λ/2 μ sin θ

     So, resolving power of microscope depends upon three factors :

    (i) Wavelength (λ) of light. Smaller the value of λ, smaller will be d and hence greater will be the resolving power. Microscope when operated in ultraviolet light gives greater resolving power than when operated in visible light. 

    (ii) Refractive index (μ) between objectives and the object. Greater value μ means smaller value of d and hence greater resolving power. To get highly resolved image we can view object after dipping it in transparent oil. 

  (iii) Value of θ. θ is the half the angle of the cone in which light from object enters the objective. Small θ, means smaller value of sin θ, smaller d and hence greater resolving power. This can be achieved by using an objective of small diameter. That is the reason why all the microscopes have small diameter objectives. 

Key words

1. Distance of distinct vision. A diameter of 25 cm for normal eye. 

2. Eye lens. The lens of eyepiece which is near the eye. 

3. Eye piece. A lens or a combination of lenses to aid eye to see final image. 

4. Focal length. Distance between principal focus and optical centre. 

5. magnification. Ratio between size of image to size of object. 

6. Magnifying power. See magnification. 

7. Microscope (simple). An ordinary convex lens. 

8. Microscope (compound). Combination of lenses to see the magnified view of objects situated nearby. 

9. Objective. Lena of optical instrument facing the object. 

10. Resolving power. Ability of the optical instrument to see two closely situated objects as separate. 

Key Formulae

1. Simple microscope. 

                 M = 1 + D/f

2. Compound microscope. 

                 M = L/fo (1 + D/fe)