94. A microscope objective has a linear magnification of 10. To achieve a final magnification of 100, the angular magnification of the eyepiece should be ________.
Compound Microscope Magnification – Complete Theory, Formula, and Detailed Numerical Solution
The compound microscope is one of the most important optical instruments studied in ray optics. It is widely used in biology, medicine, microbiology, materials science, and research laboratories to observe extremely small objects that cannot be seen clearly with the naked eye. A compound microscope produces a highly magnified image by using two convex lenses: the objective lens and the eyepiece (ocular lens).
Correct Answer
10
Understanding the Working of a Compound Microscope
A compound microscope consists of two convex lenses mounted coaxially:
- Objective Lens – Placed close to the object. It forms a real, inverted, and magnified intermediate image.
- Eyepiece Lens – Acts as a simple microscope and magnifies the intermediate image to produce the final virtual image.
The objective is mainly responsible for increasing the size of the image, while the eyepiece further enlarges that image by increasing its angular size as seen by the observer.
Magnifying Power of a Compound Microscope
The total magnifying power of a compound microscope is equal to the product of:
- The linear magnification produced by the objective.
- The angular magnification produced by the eyepiece.
Mathematically,
Total Magnification = Objective Magnification × Eyepiece Magnification
This relation shows that both lenses contribute independently to the final magnification.
Concept Used in This Numerical
The question provides:
- The linear magnification of the objective.
- The required total magnification of the microscope.
Our task is simply to calculate the angular magnification of the eyepiece using the above relationship.
Given Data
Linear magnification of objective
mo = 10
Final magnification of microscope
M = 100
Angular magnification of eyepiece
me = ?
Step-by-Step Solution
Using the relation
Total Magnification = Objective Magnification × Eyepiece Magnification
Substituting the given values,
100 = 10 × me
Therefore,
me = 100 / 10
me = 10
Verification of the Answer
If the objective magnifies the object by a factor of 10 and the eyepiece further magnifies the intermediate image by a factor of 10, then the overall magnification becomes
10 × 10 = 100
This agrees exactly with the required final magnification.
Physical Interpretation
The objective lens forms a magnified real image of the object. This image is then viewed through the eyepiece, which behaves like a simple magnifier. Because magnification occurs in two successive stages, the total magnification is obtained by multiplying the magnifications of the two lenses.
This explains why even moderate magnifications produced by individual lenses can combine to produce a very large overall magnifying power.
Real-Life Applications
Compound microscopes are indispensable in biology laboratories, hospitals, microbiology research, pathology, forensic science, nanotechnology, and materials engineering. They are used to observe cells, bacteria, blood samples, tissues, crystals, and many microscopic structures that are invisible to the unaided eye.
Exam-Oriented Key Concepts
Students should remember that the total magnifying power of a compound microscope is always the product of the objective’s linear magnification and the eyepiece’s angular magnification. The objective produces the real intermediate image, while the eyepiece magnifies that image. Questions based on this simple multiplication relation are among the most common numerical problems in ray optics.
Final Answer
The required angular magnification of the eyepiece is
10
Final Answer: 10
