Q.84 What will be value of the Numerical Aperture (NA), if half aperture angle is 58°
and oil immersed objective is used for the process of light microscopy? (Answer
up to 1 decimal place)
Consider Sin 58° = 0.85 and refractive index of immersion oil used is = 1.50.
Numerical Aperture (NA) in light microscopy with oil immersion is calculated using the formula NA = n × sin(θ), where θ is the half aperture angle and n is the refractive index of the immersion medium. Here, θ = 58°, sin(58°) = 0.85, and n = 1.50 for oil, yielding NA = 1.50 × 0.85 = 1.275, or 1.3 to one decimal place.
Calculation Steps
The standard NA formula derives from the objective’s light-gathering ability: NA = n sin(μ), where μ (half-angle) directly uses the given 58°.
Substitute values: sin(58°) = 0.85 (provided, confirmed ≈0.848 but use given).
Multiply: 1.50 × 0.85 = 1.275 ≈ 1.3.
Microscopy Context
Oil immersion boosts NA beyond air (n=1.0 limit ~1.0) by matching oil’s n≈1.51 to glass, capturing more oblique rays for higher resolution.
Typical oil objectives reach NA 1.0-1.4; this 1.3 fits high-end 60x-100x lenses.
Half-angle θ=58° allows sin(θ)=0.85, below max sin(90°)=1.0.
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Introduction
In numerical aperture half aperture angle 58 oil immersion setups for light microscopy, NA determines resolution via NA = n × sin(θ), vital for CSIR NET life sciences exams. This query uses θ=58° (half-angle), sin 58°=0.85, and oil n=1.50.
Formula Breakdown
NA = refractive index (n) × sin(half aperture angle).
n=1.50 matches glass, minimizing refraction loss.
sin(58°)=0.85 given; exact ≈0.8480.
Step-by-Step Solution
- Identify: θ=58°, n=1.50.
- Compute: sin(58°)=0.85.
- NA=1.50 × 0.85=1.275.
- Round to 1 decimal: 1.3.
No options provided, but common errors: using full angle (116°, sin>1 invalid), air n=1.0 (NA=0.85), or unrounded 1.27.
Applications in Biology
Oil immersion yields NA>1.4 max for dry, enhancing cell imaging in molecular biology. CSIR NET questions test this for microscope optics. Resolution d=0.61λ/NA improves with higher NA.
