A simple microscope is used for observing magnified images of tiny objects. It consists of a converging lens of small focal length. A virtual erect and magnified image of the object is formed at the least distance of distinct vision from the eye held close to the lens. That is why the simple microscope is also called a magnifying glass.
The course of rays through a simple microscope, F is two principle foci and C is the optical centre of the convex lens. An object AB is held between optical centre C and principle axis. A virtual, erect and magnified image A’B’ is formed as traced in fig. the eye is held close to the lens, and CB’ = d, least distance of distinct vision for the normal eye.
Magnifying power of a simple microscope is defined as the ratio of the angles subtended by image and the object on the eye, when both are at the least distance of distinct vision from the eye.
Now, the image A’B’ is already at the least distance of distinct vision (d) from the eye. Let ∠A’CB’ =β. Imagine the object AB to be displaced to A1B’ at distance d. let
∠A1CB’ = α be definition, magnifying power
m = β / α (1)
For small angles expressed in radius,
tan θ ≈ θ
Therefore, α ≈ tan α and β ≈ tan β
Therefore, m = tan α Δ/tan α (2)
In Δ ABC, tan β = AB/CB
In Δ A1B’C, tan α - A1B’/CB’ = AB/CB’
Putting in (2), we get,
m = AB/CB × CB’/AB = CB’/CB = -v/-u = v/u (3)
Where, CB’ = -u,
distance of image from the lens,
CB = -u,
Distance of object from the lens,
From the lens formula, (1/v – 1/u) = 1/ƒ
Multiply both sides by v,
1 – v/u = v/ƒ
Using (3), 1 – m = v/ƒ or m = (1 –v)/ƒ
But, v = -d,
Therefore m = (1 + d/ƒ)
This is the experimental expression for magnifying power of a simple microscope or (magnifying glass).
Also, as ƒ decreases, m increases i.e. smaller the focal length of the lens, greater is its magnifying power.
A simple microscope or magnifying glass is used:
(i) By watch makers and jewelers for having magnified view of tiny parts of watch and fine jewellery work.
(ii) By students in science laboratories for reading verniers scales etc.
(iii) The image is very bright and sharp because object is held close to the lens.
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