Microscope and it’s types

A simple magnifier or microscope is a converging lens of small focal length.

The linear magnification due to the objective is:

When the final image is at near point: \[m_e=\left(1+\frac{D}{f_e}\right)\]

When final image is at infinity: \[m_e=\left(\frac{D}{f_e}\right)\]

When the image is formed at infinity, the total magnification is:

m = \[m_om_e=\left(\frac{L}{f_o}\right)\left(\frac{D}{f_e}\right)\]

Basic Arrangement

• The lens is held near the object, one focal length away or less.
• The eye is positioned close to the lens on the other side.
• The aim is to obtain an erect, magnified, and virtual image.
• The image should be at a comfortable viewing distance, i.e. at 25 cm or more.

Image Position Cases

Case 1: Object at distance f

• If the object is at a distance f, the image is at infinity.
• This position is considered most suitable for viewing by the relaxed eye.

Case 2: Object slightly less than focal length

• If the object is at a distance slightly less than the focal length of the lens, the image is virtual and closer than infinity.
• The closest comfortable distance for viewing the image is at the near point.
• The near point distance is D ≅ 25 cm.
• Viewing at the near point causes some strain on the eye.

The linear magnification m, for the image formed at the near point D, by a simple microscope, is obtained using:

According to sign convention, vvv is negative and is equal in magnitude to D. Thus, the magnification is:

Note

• Since D is about 25 cm, to have a magnification of six, one needs a convex lens of focal length f = 5 cm.
• m = h′/h, where hhh is the size of the object and h′ is the size of the image.
• This is also the ratio of the angle subtended by the image to that subtended by the object, if the object is placed at D for comfortable viewing.
• This is not the angle actually subtended by the object at the eye, which is h / u.
• A single-lens magnifier allows the object to be brought closer to the eye than D.

To find the magnification when the image is at infinity, angular magnification is used.

Suppose the object has height h. The maximum angle it can subtend and still be clearly visible without a lens is when it is at the near point, i.e. at a distance D. The angle subtended is:

From the relations:

The angle subtended by the image is:

When the object is at u = −f,

Therefore, the angular magnification is:

Need for a Compound Microscope

• A simple microscope has a limited maximum magnification (≤ 9) for realistic focal lengths.
• For much larger magnifications, two lenses are used, one compounding the effect of the other.
• This arrangement is known as a compound microscope.

Construction and Working

• The lens nearest the object is called the objective.
• The objective forms a real, inverted, magnified image of the object.
• This image acts as the object for the second lens.
• The second lens is the eyepiece.
• The eyepiece functions essentially like a simple microscope or magnifier.
• It produces the final image, which is enlarged and virtual.
• The first inverted image is near, at, or within the focal plane of the eyepiece.
• This position is suitable for final image formation either at infinity or a little closer for image formation at the near point.
• The final image is inverted with respect to the original object.

Given:

• f_o = 1.0 cm
• f_e = 2.0 cm
• Tube length L = 20 cm

Then,

Result

• The magnification is 250.