69. An oil immersion objective of a light microscope has a numerical aperture of 1.25 . Using the Abbé
equation, the maximum theoretical resolving power (in nm) of the microscope with this objective
and blue light (wavelength = 450 nm ) is ____
Oil immersion objectives enhance microscope resolution significantly. The Abbe equation determines the theoretical limit for distinguishing fine details using blue light at a wavelength of 450 nm.
What is Resolving Power?
Resolving power measures the smallest distance between two points that appear distinct under magnification. Ernst Abbe’s equation provides this limit as:
d = 0.61λ / NA
where λ is the wavelength of light and NA is the numerical aperture. Higher numerical aperture or shorter wavelength improves resolution by reducing d.
Calculation for Given Parameters
For an objective with NA = 1.25 and blue light of wavelength λ = 450 nm, substitute into Abbe’s formula:
d = (0.61 × 450) / 1.25
d = 274.5 / 1.25 = 219.6 nm
This value is typically rounded to 220 nm as the maximum theoretical resolving power. Oil immersion increases NA beyond air objectives, enabling sub-250 nm resolution with blue light.
Common Formula Variations Explained
| Formula Variant | Expression | Use Case | Result for Query (nm) |
|---|---|---|---|
| Abbe’s Standard | d = 0.61λ / NA | Theoretical limit for periodic structures | 220 |
| Simplified | d = λ / (2NA) | Practical approximation (ignores 0.61 factor) | 180 |
| Full System | d = λ / (NAobj + NAcond) | When condenser NA matches objective | Varies (e.g., 180 nm if both 1.25) |
Since the question specifies only the objective’s numerical aperture, Abbe’s standard formula applies directly. Variants arise from different diffraction assumptions but converge near 200 nm for these parameters.
Factors Affecting Real-World Resolution
- Immersion oil increases NA up to ~1.4 by matching refractive index.
- Blue light (450 nm) provides better resolution than red due to shorter wavelength.
- Aberrations and optical imperfections raise practical limits above theory.
Despite real-world limitations, 220 nm remains the accepted theoretical benchmark.
Correct Answer
220 (integer fill-in-the-blank format)
