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Simple Microscope

Definition of Simple Microscope

A simple microscope or magnifying lens is a convex lens of short focal length.

Principle of Simple Microscope

When an object is placed in front of a convex lens between the optical center and focus on the principal axis, a virtual, erect and magnified image of the object is formed.

Ray diagram of a simple microscope

In the figure AB is a small object which is placed between the optical center (O) and focus (F) of a convex lens, due to which a magnified, erect and virtual image of the object is formed. This image forms an angle β at the eye of the observer (when seen in the picture, this angle appears to be formed at the optical center, but because the eye of the observer is very close to the optical center, hence this angle is also called the angle formed at the eye). In the second picture, the same object AB has been placed in front of the observer’s eye at the least distance of distinct vision (D) due to which an angle α is formed at the eye (This second picture is to compare what angle the object would subtend at the eye of the observer if he did not have a simple microscope).

Magnifying Power of Simple Microscope

The magnifying power of a simple microscope is defined as the ratio of the angle subtended at the eye by the image (β) to the angle subtended by the object at the eye (α), i.e.,

$\displaystyle m=\frac{\beta }{\alpha }$

The angles β and α are very small, hence $\displaystyle \beta \approx \text{tan}\beta ,\text{ }\alpha \approx \text{tan}\alpha$

$\displaystyle \Rightarrow m=\frac{\text{tan}\beta }{\text{tan}\alpha }$ …..(1)

In the triangle ABO in the figure,

$\displaystyle \text{tan}\beta =\frac{AB}{OB}$ …..(2)

Similarly in triangle ABE,

$\displaystyle \text{tan}\alpha =\frac{AB}{EB}$ …..(3)

Putting the values of equations (2) and (3) in equation (1),

$\displaystyle m=\frac{{}^{\text{AB}}\!\!\diagup\!\!{}_{OB}\;}{{}^{AB}\!\!\diagup\!\!{}_{EB}\;}$

$\displaystyle \Rightarrow m=\frac{AB}{OB}\times \frac{EB}{AB}$

$\displaystyle \Rightarrow m=\frac{EB}{OB}$ …..(4)

Using sign conventions,

EB = -D व OB = -u

By putting the values of EB and OB in equation (4),

$\displaystyle m=\frac{-D}{-u}$

$\displaystyle \Rightarrow m=\frac{D}{u}$ …..(5)

Equation (5) is the general formula for the magnifying power of a simple microscope. For different values of u, different values of magnifying power will be obtained. Let us now find the value of magnifying power in some special cases.

Special cases

(1) When the final image is formed at the least distance of distinct vision (D)

In this situation,

u = -u , v = -D and f = +f

From lens formula,

$\displaystyle \frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$\displaystyle \Rightarrow \frac{1}{f}=\frac{1}{-D}-\frac{1}{(-u)}$

$\displaystyle \Rightarrow \frac{1}{f}=\frac{1}{-D}+\frac{1}{u}$

$\displaystyle \Rightarrow \frac{\text{D}}{f}=\frac{D}{-D}+\frac{D}{u}$

$\displaystyle \Rightarrow \frac{\text{D}}{u}=1+\frac{\text{D}}{f}$

From equation (5),

$\displaystyle m=1+\frac{D}{f}$ …..(6)

It is clear from equation (6), that lower the value of focal length f of the lens, higher will be the magnifying power (m). For this reason, in the definition of a simple microscope, its focal length has been described as short.

(2) When the final image is formed at infinity (∞)

To form the final image at infinity, the object must be placed at the focus point in front of the convex lens. Hence, by substituting u = f in equation (5),

$\displaystyle \Rightarrow m=\frac{D}{f}$ …..(7)

[Here you may wonder why u = -f was not kept! Note that when we derived equation (5), the negative sign was already placed while placing OB = -u]

Note :- The magnifying power in equation (7) is one less than equation (5), but seeing the image formed at infinity is relatively more comfortable and the difference in magnification is also relatively less. Therefore, if we have to work for a longer time with a simple microscope, then we will prefer the image formed at infinity and the magnifing power will be given by equation (7). Whereas if work has to be done for less time and more magnifying power is required, then we will give priority to the image made at the least distance of distinct vision (D) and use the magnifying power formula of equation (5).

Uses of Simple Microscope

Reading small text: Simple microscopes are often used to read small text in books, newspapers, or documents, especially for visually impaired people.
Inspecting Jewelry and Gemstones: Jewelers and gemologists use simple microscopes to closely examine the features and imperfections of gems, diamonds, and other precious materials.
Watchmaking/Repair and Precision Work: Watchmakers and individuals involved in precision craftsmanship use simple microscopes to inspect and repair small components in watches, microelectronics, and other devices.
Education: Simple microscopes are used to introduce students to the principles of microscopy and to study small objects/specimens/Vernier scales in science classes.