Principle Construction, Working and Angular Magnification of Compound Microscope
Principle: The principle of the compound microscope is based on the magnification of an image by using two lenses.
Construction: A compound microscope consists of two convergent lenses (i.e. objective lens O and eye-piece lens e) placed coaxially in a double tube system. The objective lens is an achromatic convergent lens system of short focal length and short aperture. The other eye-piece lens e is also an achromatic convergent lens system of large focal length and large aperture. The observation is taken through the eye-piece lens by the observer. The eye-piece lens is fitted outer side of a movable tube and the inner side connects with a non-movable tube in which the objective lens is fitted on another side of the non-movable tube. The separation between the objective or eye-piece lens can be changed by an arrangement, this is known as rack and pinion arrangement.
Working: Suppose a small object ab is placed slightly away from the first focus f∘ of the objective lens which forms a real, inverted, and magnified image a1b1. Now adjust the eye-piece lens by moving like this, that the image a1b1 lies in between the optical center and the second focal length fe of the eye-piece lens. This image a1b1 works as an object for the eye-piece lens which forms a magnified, virtual, and final image a2b2. The final image a2b2 is generally formed at the least distance D of distinct vision, although it can be formed anywhere between this position and infinity.
Angular Magnification Or Magnifying Power(M):
The angular magnification or magnifying power can be defined as the ratio of the angle subtended by the image at the eye (β) to the angle subtended by the object at the eye when placed at least distance of distinct vision (α)
M=Anglesubtendedbytheimageattheeye(β)Anglesubtendedbytheobjectattheeyewhenplacedatleastdistanceofdistinctvision(α)
M=βα≈tanβtanα(1)
From figure
tanβ=a2b2a2e
tanα=a2a3a2e
Now subtitute these values in equation (1), then
M=a2b2a2ea2a3a2e
M=a2b2a2a3
Here a2a3=ab
So the above equation can be written as
M=a2b2ab
M=a2b2aba1b1a1b1
M=a2b2a1b1a1b1ab
Here me=a2b2a1b1 and m∘=a1b1ab
Now substitute the values of me and m∘ in the above equation
M=me×m∘(1)
Where
me→ The linear magnification produced by eye-piece lens system
m∘→ The linear magnification produced by the object lens system
So now again from the figure
The linear magnification produced by object lens system m∘=−v∘u∘
The linear magnification produced by eye-piece lens system me=Due
Substitute the value of m∘ and me in equation (1)
M=−v∘u∘(Due)(2)
Adjustment of a Compound Microscope:
1.) Adjustment for Clear Vision: In this final image an object is formed at least a distance of distinct vision D. For this configuration,
On substitution u=−ue, v=−D and f=fe in the lens formula for eyepiece lens
1−D+1ue=1fe
1ue=1fe+1D
Due=(Dfe+1)
Now substitute the value of Due in equation (2)
M=−v∘u∘(1+Dfe)
The length of the microscope tube in this setup
L= Distance between the object and the eye-piece lenses
L=v∘+|ue|
2.) Adjustment for Relaxed Eye: In this configuration, the final image of an object is formed in a relaxed eye position i.e. at ∞. In this setup, the eye-piece lens system is moved back until the image of object ab, formed by object lens,i.e., a1b1 fall at (coincide with)second focus f′e of the eye-piece lens system. Mathematically this situation comes when ue=fe
Thus, the magnifying power in this position,
M=−v∘u∘(Dfe)
For this set the length of the microscope tube,
L=v∘+fe
me→ The linear magnification produced by eye-piece lens system
m∘→ The linear magnification produced by the object lens system