Calculating Limit of Resolution in a Compound Microscope: Detailed Guide

Introduction

The resolving power of a microscope is one of the most vital properties in scientific research. It determines how fine the details are that can be distinguished between two points under observation. When using a compound microscope, several factors combine to set this limit—chiefly the wavelength of light, the refractive index of the observation medium, and the sine of the angular aperture. Let’s explore the physics and calculations behind the limit of resolution and illustrate why 0.216 µm is the correct answer for your scenario.

The Science Behind Resolution

What is Resolution?

• Resolution is the ability to distinguish two adjacent points as separate entities.

• It controls image clarity and the amount of cellular, tissue, or material detail observable under the microscope.

Formula for Limit of Resolution

The most widely used formula, based on Abbe’s diffraction limit, is:

D=0.61λ/ nsin⁡α

Where:

• $D$: Limit of resolution (the minimum resolvable distance, in micrometers µm)

• λ: Wavelength of incident light (in µm)

• $n$: Refractive index of the medium between lens and specimen

• sin⁡α: Sine of half the angular aperture of the objective lens

Smaller D = better resolving power.

Calculation: Step-by-Step

Given:

• λ = 500nm = 0.5µm

• $n$ = 1.5 (oil immersion medium)

• sin⁡α= 0.94

Plug the numbers into the formula:

D=0.61×0.5 /  1.5×0.94

Correct answer: (1) 0.216 µm

Why These Parameters Matter

1. Wavelength (λ) of Light

• Shorter wavelengths (e.g., blue light) yield greater resolution.

• Longer wavelengths limit the ability to see fine details.

2. Refractive Index (n)

• Higher refractive index media (like oil) increase the light-gathering ability and resolution.

• Air objectives (with n=1.0) resolve less detail compared to oil immersion objectives (n∼1.5).

3. Angular Aperture ($\alpha$)

• A larger value for $\sin \alpha$ indicates that the objective lens gathers light from a wider angle, improving resolution.

• High NA objectives are specifically designed for sharper images and oil immersion use.

Practical Importance

• A limit of resolution of 0.216 µm means you can distinguish points separated by at least this distance, essential for fine cellular and sub-cellular imaging.

Common Errors in Resolution Calculation

• Confusing magnification with resolution: Magnification just makes things bigger, resolution makes details clear.

• Using incorrect unit conversions: Always convert nm to µm for consistency.

• Ignoring the importance of NA: Both the refractive index and the sine of the angular aperture must be considered together ().

Enhancing Resolution in the Lab

How to Achieve Maximum Resolution

• Use the shortest practical wavelength light.

• Oil immersion objectives for high NA.

• Keep optics clean and properly aligned.

• Use correct coverslip thickness and adjust condenser for optimal image sharpness.

Table: Impact of Each Factor on Resolution

Modern Application: Why Resolution Matters

• Cell Biology: See structures as small as bacteria, mitochondria, and chromosomes.

• Histology: Distinguish cellular boundaries and tissue types with precision.

• Material Science: Resolve nanoparticles, fibers, and other microscopic features.

The Importance of Oil Immersion Objectives

Oil immersion not only improves resolution by increasing the refractive index, but also minimizes loss of light due to refraction between the glass slide and objective lens. This makes oil immersion objectives essential in high-powered biological research ().

Common Mistakes to Avoid

• Using water or other low-index liquids instead of oil for objectives designed for oil immersion.

• Overlooking the role of wavelength or defaulting to higher wavelengths (red/yellow light) that give lower clarity.

• Not factoring in both refractive index and angular aperture when calculating resolution limit.

FAQs

Q: Does higher magnification always mean higher resolution?

• No, true clarity comes from higher NA and lower D, not just increased size.

Q: Can resolution be improved indefinitely?

• Classical optics are limited by diffraction; electron and super-resolution microscopes can surpass this limit.

Q: Why is oil preferred over air or water?

• Oil’s refractive index closely matches glass, limiting distortion and maximizing NA.

Conclusion

With a wavelength of 500nm, refractive index of 1.5, and sinα of 0.94, the limit of resolution for the microscope is 0.216 µm. This result is grounded in the optical physics of microscopy and illustrates the direct relationship between these parameters and image clarity.

Always use the correct formula, pay attention to units, and leverage oil immersion objectives for the finest possible scientific detail in microscopy.