26. To achieve the best resolution using a fluorescence microscope, what combination of wavelength of emitted light (λ), refractive index and the angle (2θ) by which light enters into the microscope would be the best choice?
A. λ = 405 nm; refractive index = 1.33; 2θ = 90°
B. λ = 420 nm; refractive index = 1.51; 2θ = 180°
C. λ = 520 nm; refractive index = 1.51; 2θ = 90°
D. λ = 405 nm; refractive index = 1.51; 2θ = 180°
Correct Answer: D. λ = 405 nm; refractive index = 1.51; 2θ = 180°
Fluorescence microscope resolution follows d ≈ λ / (2 NA), with NA = µ sin(θ) where θ is half-angle (2θ = full angular aperture). Option D minimizes d via shortest emitted λ (405 nm), highest µ (1.51 oil), and max sin(θ) = sin(90°) = 1 from 2θ=180° (θ=90°).
Resolution Calculation Comparison
Lower d = better resolution. Compute relative d ∝ λ / µ sin(θ):
| Option | λ (nm) | µ | θ (°) | sin(θ) | Relative d ∝ λ/(µ sinθ) |
|---|---|---|---|---|---|
| A | 405 | 1.33 | 45 | 0.707 | 405/(1.33×0.707) ≈ 430 |
| B | 420 | 1.51 | 90 | 1.0 | 420/(1.51×1.0) ≈ 278 |
| C | 520 | 1.51 | 45 | 0.707 | 520/(1.51×0.707) ≈ 487 |
| D | 405 | 1.51 | 90 | 1.0 | 405/(1.51×1.0) ≈ 268 |
D yields the smallest d (~268 arbitrary units).
Option Explanations
A: Short λ good, but low µ=1.33 (water) and small sin(45°)=0.707 limit NA~0.94; poor resolution.
B: Max NA good (oil, full aperture), but longer λ=420 nm worsens vs. D.
C: Oil good but small θ=45° caps NA~1.07; longest λ=520 nm (green emission) disastrous.
D: Optimal—violet λ=405 nm, oil µ=1.51, max aperture θ=90° for NA~1.51.
Fluorescence Resolution Principles
Fluorescence microscope resolution optimizes via shortest emitted wavelength λ, highest refractive index µ, and largest angle 2θ for max NA=µ sin(θ). Option D (405 nm, 1.51, 180°) excels, ideal for super-res imaging in GATE Life Sciences.
Parameter Impact Table
| Parameter | Best Choice | Why? |
|---|---|---|
| Emitted λ | 405 nm | ↓λ directly ↓d |
| Refractive Index µ | 1.51 oil | ↑NA 50% over water/air |
| Angle 2θ | 180° (θ=90°) | sin90°=1 max capture angle |
GATE Applications
Confocal/TIRF fluorescence hits ~200 nm with oil objectives; compare options via d ∝ λ/NA. Shorter λ suits violet dyes despite photobleaching risks.
