Numerical Aperture (NA) and Resolving Power of a Microscope -Wave Optics Class 12 Physics for NEET Exam

Numerical Aperture (NA) and Resolving Power of a Microscope

Why “making it bigger” is useless if you can’t capture detail 🔬

Many NEET students think a microscope’s main job is to make objects look bigger. But imagine this: you take a photo of a friend standing far away, then zoom the photo 10 times. Do you suddenly see the eyelashes clearly? No. You only see a bigger blur.

This is the key idea in microscopy:

Magnification only makes the image bigger.
Resolution decides whether you can see fine details.

So before you study “resolving power”, you must understand the concept that controls resolution at the most basic level: Numerical Aperture (NA).

1) What is Numerical Aperture (NA)?

Numerical aperture is a measure of how much light an objective lens can collect from the specimen.

Think of the objective lens like a “light collector”. If it collects more light rays, the image becomes:

• brighter

• clearer

• more detailed

• better resolved (two close points can be seen separately)

The formula is:

NA = μ × sin α

Where:

• μ (mu) = refractive index of the medium between the objective lens and the specimen

• α (alpha) = half-angle of the cone of light entering the objective lens

Important: α is the half-angle, not the full cone angle.

2) Why NA matters more than magnification

If the microscope does not capture enough detail, enlarging the image does nothing.

So the correct order is:

1. First, capture detail → needs high NA

2. Then, enlarge it → magnification

That’s why NA is considered a “core foundation” before resolving power.

3) The “cone of light” idea (very important)

Light from the specimen enters the objective lens in the shape of a cone.

• If the cone is narrow → α is small → sin α is small → NA is small

• If the cone is wide → α is large → sin α is large → NA is large

So, a lens with a wider acceptance angle can capture more rays and therefore produce a sharper image.

In theory, the best case would be a very wide cone where α approaches 90 degrees.
Because sin 90 = 1 (maximum possible value).

In real biological microscopes, the angular aperture is usually around 70 to 80 degrees, which is still quite large, giving a high NA.

4) NA and image brightness

Higher NA also means more light is collected. That improves brightness and contrast.

So when NA is low, you commonly see:

• dim image

• low contrast

• poor clarity

• fine details merging together

When NA is high:

• image becomes brighter

• edges look sharper

• tiny details become visible

5) Why oil immersion increases NA

In many microscopes, the medium between objective and specimen is air.

Refractive index of air:

• μ ≈ 1.0

So in air:

• NA = 1 × sin α = sin α
  That limits how high NA can go.

To increase NA, we increase μ.
So we replace air with immersion liquid like:

• immersion oil

• glycerine (in some cases)

Immersion oil has refractive index close to glass:

• μ ≈ 1.5

So:

• NA = 1.5 × sin α

That is a big improvement, and it directly improves resolution.

6) The cover slip refraction problem (and how oil fixes it)

In biology, the specimen is usually covered with a thin glass cover slip.

Now light has to travel through multiple media:

• specimen (watery)

• glass cover slip

• air

• objective lens

Whenever light goes from one medium to another with different refractive index, it bends (refraction).
This refraction can disturb the light path and reduce clarity.

If the refractive index difference is large (like glass to air), light bends strongly and some rays do not even enter the objective lens properly. This reduces NA and reduces resolution.

Solution: Fill the gap between cover slip and objective with immersion oil whose refractive index is close to glass.

Result:

• less refraction disturbance

• more rays enter the lens

• NA increases

• image becomes sharper and more detailed

So oil immersion is not “just a fancy extra”. It is a real optical improvement.

7) NA and resolving power (NEET concept)

Resolving power means the ability of a microscope to distinguish two very close points as separate.

If two points are extremely close, they may appear as one blurred spot. This happens because of diffraction and the limitations of the optical system.

The resolving ability depends mainly on:

1. Numerical aperture (NA)

2. Wavelength of light (λ)

NEET-level takeaway:

• Higher NA → better resolution

• Smaller wavelength → better resolution

In simple words:

• If the lens collects rays from wider angles and through a higher refractive index medium, it can separate details more clearly.

8) Why high-NA microscopes are expensive

Microscopes with high NA require:

• precision lens manufacturing

• special glass and coatings

• better aberration control

• immersion setups

• tight engineering tolerances

That’s why high-NA objectives can be expensive and used mainly in advanced microscopes.

So there is a clear trade-off:
High NA = high resolution = high cost

9) Quick NEET notes (high scoring lines)

• Numerical aperture decides light-gathering power and resolution of a microscope.

• NA formula: NA = μ sin α

• Oil immersion increases NA because μ increases.

• Higher NA gives:

  • brighter image

  • better contrast

  • better resolution

• Magnification without NA is useless. You get a bigger blur, not more detail.

10) Common mistakes students make

Mistake 1: Oil immersion increases magnification
Correct: Oil immersion mainly increases NA, improving resolution.

Mistake 2: Resolution depends only on magnification
Correct: Resolution depends on NA and wavelength.

Mistake 3: NA depends only on lens design
Correct: NA depends on both α (lens angle) and μ (medium).

Final takeaway

If you remember only one line, remember this:

Numerical aperture decides how much “detail-carrying light” enters the microscope. If NA is low, magnification gives only a bigger blur.