We all have used microscopes in our school laboratory
These optical instruments made it possible for us to see and study tissues and cells of plants
In order to study the cells, a simple microscope would not suffice with it's limited magnification of 40X
To magnify beyond 40X, a second lens is added to a simple microscope. This set up is called a compound microscope
The two lenses in a compound microscope are called Objective and Eyepiece lens
The lens through which the final image is observed is called the eyepiece lens whereas the lens just above the object is called the objective
The combination of lenses in a compound microscope allows magnification in the range of 40×→1000×
Let us understand the working principle of a compound microscope
The object AB is placed outside the focus of the objective lens (F1). The objective lens forms a real, magnified and inverted image A1B1
The image A1B1 becomes the object for the second lens, the eyepiece
The distance between the two lenses is adjusted such that the image A1B1 lies within the focus of the eyepiece, F2
The eyepiece forms a magnified, virtual and inverted (as compared to the original object) image
Hence together, the lenses in a compound microscope produce a highly magnified, virtual and inverted image of the object
Let us see how the formula for magnification by a compound microscope can be obtained
We know the magnifying power (M) is defined as - M=αβ
β is the angle subtended by the final magnified image on the eye; whereas α is the angle subtended by the original object on the eye when placed at the least distance of distinct vision
From the ray-diagram, we can see that β=ueA1B1=veA2B2
From the figure, α=DAB
We can then calculate the magnifying power, M=αβ
Re-arranging the terms M=ABA1B1×ueD
We know,A1B1=voAB=uo∴M=−uovo×ueD-ve sign is used for uoaccording to the sign-convention
Therefore we can write M=−uovo×ueD
Applying the lens formula on the eyepiece, fe1=ve1−ue1
According to the sign-convention ve and ue will be negative
Therefore the lens formula becomes fe1=−ve1−−ue1→ue1=fe1+ve1
Using the value of ue1we can write M=−uovo(feD+veD)
Now there can be two cases regarding the final image
When the final image is at D, ve=DM=−uovo(1+feD)
M, in this case, can also be written as M=uo−fofo(1+feD)
When the final image is at infinity, ve=∞M=−uovo×feD
Revision
The magnifying power (M) of a compound microscope when the final image is formed at D is given by, M=−uovo(1+feD)
The magnifying power (M) of a compound microscope when the final image is formed at D is also given by, M=uo−fofo(1+feD)
The magnifying power (M) of a compound microscope when the final image is formed at infinity is given by, M=−uovo×feD