Compound Microscope, Working, Magnification, Practice Problems, FAQs.

Simple microscope has its limitation as it can magnify only up to 10X. For viewing a very small sample we need a microscope having higher magnification. Higher magnification can be obtained by using multiple converging lenses. When two convex lenses are placed together its magnification gets multiplied. This system is known as a compound microscope. In this topic we will know about the working and magnification of a compound microscope!

Table of content

• What is a compound microscope?
• Working of compound microscope
• Magnification of compound microscope
• Practice problems
• FAQs

What is a Compound Microscope?

A compound 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.

Working of Compound Microscope

As shown in figure the lens near the object is called the objective which forms a real, inverted, magnified image of the object. This image serves as the object for the second lens. The lens which is used to view the final image is called an eyepiece, which functions like a simple microscope or magnifier. It produces an image, which is enlarged and virtual. When the final image is formed at a near point, the first inverted image will be within focal distance (As shown in figure).

When the final image is formed at infinity the first inverted image will be at focal distance.

The final image is inverted with respect to the original object. Now let's obtain the magnification due to a compound microscope.

Magnification of Compound Microscope

For compound microscope Magnification is defined as a ratio of size of final image to the size of object.

Referring the below figure

Magnification due to objective lens

Now 

And

So,

When object is seen without lens

Putting the value of and in equation (i)

Where m_o is magnification due to objective lens and m_e is the magnification due to the eyepiece.

Now consider two cases

Case-1 When the final image is formed at near point 

Now for eyepiece using the lens formula

From equation (iv)

Magnification

This is the formula for magnification when the final image is viewed at a near point.

Case-2 When the final image is formed at infinity. 

Again using the lens formula

From equation (iv)

Magnification

This is the formula for magnification when the final image is viewed at infinity.

Practice Problems

Q1.The focal length of the objective is 0.5 cm and the focal length of the eyepiece is 5 cm. The image of the object is formed at a distance of 15.5 cm from the objective. If the final image is formed at a near point, find the magnifying power of the microscope?

Answer: Given f_e=5 cm

f_o=0.5 cm

v_o=15.5 cm

Using lens formula for objective lens

When image formed at near point magnification is given by

m=-180 Ans

Q2. The magnification of the objective lens of a compound microscope is 10. To get an overall magnification of 100 when the image is formed at 25 cm from the eye, the focal length of the eye lens should be?

A. 4 cm
B. 10 cm
C.
D. 9 cm
Answer: Given M₀=10

M=100

D=25 cm

When image formed at near point magnification is given by

Hence, the option (C) is correct.

Q3.The separation of the objective (f_o=0.5 cm) and the eyepiece (f_e=5 cm) in a compound microscope is L= 7 cm. Where should a small object be placed so that the eye can see the image without strain and what is the magnification ?
Answer: The eye will see the image without strain if the final image is formed at infinity. In this case, the image formed by the objective should fall at the focus of the eyepiece.

As f_e=5 cm, L=7 cm, the first image will form at a distance = 7−5=2 cm from the objective.

So, v_o=2 cm, also f_o=0.5 cm

For objective using lens formula

The object should be placed at from objective.

Magnification

Q4. In a compound microscope, the focal length of an objective lens is 1.2 cm and the focal length of the eyepiece is 3 cm. When the object is kept at 1.25 cm in front of the objective, final image is formed at , the magnification power is?

A. 100
B. 200
C. 300
D. 400

Answer: Given u_o=-1.25 cm

f_e=3 cm

f_o=1.2 cm

Using lens formula for objective lens

v_o=30 cm

When image formed at infinity magnification is given by

m=-200

m=200

Thus (B) is the correct answer.

FAQs

Question 1. How is the compound microscope different from a simple microscope?
Answer:  A compound microscope has different lenses, the objective lens has (typically 4x, 10x, 40x or 100x) and the eyepiece lens (typically 10x). So a high magnification of 40x, 100x, 400x and 1000x can be obtained.

Question 2. How much smaller things a compound microscope can see?
Answer: Compound microscopes can magnify the specimens such as cells, bacteria, algae, protozoa etc.

Question 3. Why is the objective lens small in compound microscopes?
Answer: Compound microscopes are used to see small objects situated nearby. If the aperture is larger, then light rays coming from the object will expand and the object will be seen dim.

Question 4. What is the working distance of a compound microscope?
Answer: The distance between the front of the objective lens and specimen surface when the specimen is focused.