Compound Microscope

• Acompound microscope is an optical instrument which uses two sets of lenses

providing a high resolution and 2-dimensional image of the sample.

• Compound microscope is one type of optical microscope; the other type is a

simple microscope. The difference between a simple and a compound

microscope is that a simple microscope uses one lens whereas a compound

microscope uses two or more lenses. The figure below shows a compound

microscope with its various parts.

• A Compound microscope is composed of two convex lenses of short focal

lengths placed in a tube. The two lenses are separated by a certain fixed

distance.

• The diagram of a compound microscope is shown in Figure below. The lens

near the object, called the objective, forms a real, inverted, magnified image

of the object. This serves as the object for the second lens which is the

eyepiece. Eyepiece serves as a simple microscope that produces finally an

enlarged and virtual image. The first inverted image formed by the objective is

to be adjusted close to, but within the focal plane of the eyepiece so that the

final image is formed nearly at infinity or at the near point. The final image

is inverted with respect to the original object. We can obtain the magnification

for a compound microscope.

How compound microscope works to produce the final image

• Consider two lenses in succession as shown in figure below.

• The object is just beyond the focal length of the objective lens, producing a real,

inverted image that is larger than the object. This first image serves as the

object for the second lens, or eyepiece. The eyepiece is positioned so that the

first image is within its focal length so that it can further magnify the image.

In a sense, it acts as a magnifying glass that magnifies the intermediate image

produced by the objective. The image produced by the eyepiece is a magnified

virtual image. The final image remains inverted but is farther from the observer

than the object, making it easy to view.

• The eye views the virtual image created by the eyepiece, which serves as the

object for the lens in the eye. The virtual image formed by the eyepiece is well

outside the focal length of the eye, so the eye forms a real image on the retina.

Magnification produced by a compound microscope

풉

풉^′



From

the

Figure

above,

,

′

풉

풉′

푳

Then,

• Here, the distance L is between the first focal point of the eyepiece to the

second focal point of the objective. This is called the tube length L of the

microscope as 풇_푶and 풇_풆are comparatively smaller than L

• If the final image is formed at P (near point focusing), the magnification 풎_풆

of the eyepiece is,

• Also here, 풇_푶and 풇_풆are the focal lengths of the Objective and the eyepiece,

respectively. We assume that the final image is formed at the near point of

the eye, providing the largest magnification. Note that the angular

magnification of the eyepiece is the same as obtained earlier for the simple

magnifying glass. This should not be surprising, because the eyepiece is

essentially a magnifying glass, and the same physics applies here.

• Therefore, the net magnification (풎) in near point focusing of the

compound microscope is the product of the linear magnification of the

objective and the angular magnification of the eyepiece

• If the final image is formed at infinity (normal focusing), the first inverted

image will be at focal distance of the eyepiece,

From lens formula;

, whereby

(thus; at infinity

)

From;

, but;

………… multiply by D each side of the equation

Thus; the magnification

of the eyepiece at infinity is,

 Therefore, the total magnification m in normal focusing (at infinity) is,

Worked Examples

1. A microscope has an objective and eyepiece of focal lengths 5 cm and 50 cm

respectively with tube length 30 cm. Find the magnification of the microscope in

the (i) near point and (ii) normal focusing.

ANS; given;

(iii)At near point,

(iv)

At normal focusing,

2. A compound microscope has an objective and an eyepiece separated by a

distance of 180 mm and having focal lengths of 6 mm and 30 mm respectively.

Where must an object be placed so that the final image, as seen through the

eyepiece, is formed at infinity?

ANS;

NB; when the final image is formed at infinity, the first image of the objective

lens must be formed at the focus (focal point) of the eyepiece lens

Consider the figure below

푳 = 풗_풐+ 풇_풆

Then;

풗_풐= 푳 − 풇_풆=

− ퟑퟎ

1

25−1

150

24

4

From;¹

=

→

=

−

= ¹₆− ₁₅₀

=

→

풇_풐

풖_풐풗_풐

풖_풐

풇_풐

풗_풐

150

25

ퟏퟖퟎ

1

4

=

→ 풖_풐= ퟔ. ퟐퟓ

=150mm

풖_풐

25

mm

Therefore; the object must be placed 6.25 mm from the objective lens, so as

the final image is formed at infinity

3. 5 An object sits 35 cm to the left of a converging lens with focal length of 20

cm. 75 cm to the right is a second converging lens with focal length of 15

cm. Locate and characterize the final image.

ANS;

Consider the figure below

From the first lens;

cm

But; 퐿 = 풗_ퟏ+ 풖_ퟐ 풖_ퟐ= 푳 − 풗_ퟏ= ퟕퟓ − ퟒퟔ. ퟕ= 28.3cm

This image (which is real, inverted, and enlarged) becomes the object for the

second lens then we again apply the Image Equation,

cm

That is, the final image is located 31.9 cm to the right of the second lens. Since;

풗_ퟐ풊풔 + 풗풆, the image formed is real . It is inverted, compared to the object for

lens 2. But that was an inverted image of the original object. Therefore, this final

image is upright. The total magnification is the product of the magnifications of

the two lenses,

4. A compound microscope has an objective lens of focal length 2 cm and eye piece

of focal length of 6 cm. An object is placed 2.4 cm from the objective lens. If the

distance between the objective lens and the eyepiece lens is 17 cm find the

distance of the final image from the eyepiece.

Soln: Given: 풇_풐= 2 cm, 풇_풆= 6 cm, 풖_풆= 2.4 cm, 푳 = 17 cm

Consider the figure below:

Refraction from the objective lens:

From:

풗_풐= ퟏퟐ풄풎, but 풗_풐+ 풖_풆= 푳 → 풖_풆= 푳 − 풗_풐= ퟏퟕ − ퟏퟐ = ퟓ풄풎

Also consider the refraction from the eyepiece lens

From:

D = -30 cm, (According to real – is – positive the final image is virtual)

∴ The distance of the final image from the eyepiece is 30 cm

5. Calculate the magnification of an object placed 6.20 mm from a compound

microscope that has a 6.00 mm focal length objective and a 50.0 mm focal length

eyepiece. The objective and eyepiece are separated by 23.0 cm.

ANS;

Given; 풖_푶= ퟔ. ퟐ풎풎 , 풇_푶= ퟔ. ퟎ풎풎, 풇_풆= ퟓퟎ. ퟎ풎풎, 푳 = ퟐퟑퟎ풎풎

Refraction from the objective lens:

From:

mm

But; 푳 = 풖_풆+ 풗_풐→ 풖_풆= 푳 − 풗_풐= ퟐퟑퟎ − ퟏퟖퟔ = ퟒퟒ풎풎

Refraction from the eyepiece lens:

From:

NB; negative sign means, the final image is virtual and erect with respect to the

first image

Therefore; total magnification is given by

6. A compound microscope consists of two thin converging lenses. The focal

length of the objective lens is 10 mm and that of the eyepiece lens is 20mm.

If an object is placed 11mm from the objective lens, the instrument

produces an image at infinity. Calculate the separation of the lenses and

the magnifying power of the instrument

ANS: Given;

From;

But; when image at infinity;

mm

7. The total magnification produced by a compound microscope is 20. The

magnification produced by the eye piece alone is 5. The microscope is focused

on a certain object. The distance between the objective lens and the eyepiece is

observed to be 14 cm. If least distance of distinct vision is 20 cm, calculate the

focal lengths of the objective and eyepiece lenses.

ANS;

Given:

,

=?,

=?

From:

For distance of near vision,

From eqn (i)

,

substitute m_e= 5 in eqn (ii)

cm

and

8. The objective and eyepiece of a compound microscope are 24cm apart.

Suppose the focal lengths of the objective and the eyepiece are 3cm and 9cm

respectively. (a) Where must a specimen be located to produce a final virtual

image at infinity?

(b) What could be the total magnification of this microscope? (Assume a

microscope is used by a person whose nearest distance for a distinct vision is

25cm).

풗_풐= 푳 − 풇_풆= 24 − 9 = 15푐푚, 푓푟표푚; _푓= + _푣

푢

(a)

cm

ANSW: Given;