# Numerical Aperture Calculator NA = n·sinα with the full acceptance cone and Abbe limit λ/(2·NA) — dry versus oil-immersion microscopy. > Canonical page: https://elysiatools.com/en/tools/numerical-aperture-calculator - **Category:** Science & Education - **Keywords:** numerical aperture, acceptance angle, abbe limit, microscope resolution, oil immersion, optics ## Overview Calculate the numerical aperture (NA) of microscope objectives and optical systems using medium refractive index and acceptance angle. The tool computes the total acceptance cone, numerical aperture via NA = n·sinα, and the diffraction-limited Abbe resolution limit for any specified illumination wavelength. ## Inputs - **Medium refractive index n** (number): e.g. 1.0 - **Half acceptance angle α (degrees)** (number): e.g. 30 - **Wavelength λ (nm, optional)** (number): e.g. 550 ## When to use - Determining light gathering capacity and lateral resolution limits for dry or immersion microscope objectives. - Evaluating light coupling acceptance cones and numerical aperture for optical fibers and condenser lenses. - Comparing diffraction-limited resolving power across different immersion media like air, water, and immersion oil. ## How it works - Enter the refractive index (n) of the medium between the objective lens and sample. - Specify the half acceptance angle (α) in degrees to calculate the light collection cone and numerical aperture (NA = n·sinα). - Optionally provide the illumination wavelength (λ) in nanometers to compute the theoretical Abbe diffraction resolution limit (d = λ / (2·NA)). ## Use cases - Microscopy objective selection: Evaluating whether a dry, water, or oil immersion lens meets the required resolution threshold. - Optical fiber acceptance angle analysis: Computing numerical aperture and half-angle boundaries for efficient light coupling. - Fluorescence microscopy planning: Calculating diffraction-limited spot sizes for specific fluorophore emission wavelengths. ## Frequently asked questions ### What is numerical aperture (NA)? Numerical aperture is a dimensionless measure of an optical system's ability to gather light and resolve fine specimen detail, defined as NA = n·sinα. ### Why can a dry objective not exceed an NA of 1.0? In air (n ≈ 1.0), sinα reaches a maximum theoretical value of 1 at 90°, making an NA greater than 1.0 physically impossible without immersion media. ### How does immersion oil improve optical resolution? Immersion oil has a refractive index close to glass (n ≈ 1.515), preventing light refraction at the coverslip and enabling higher acceptance angles and higher NA values. ### How is the Abbe resolution limit calculated? The lateral Abbe resolution limit is calculated using the formula d = λ / (2·NA), where λ is the light wavelength and NA is the numerical aperture. ### Is the wavelength field mandatory? 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