1. What is a Numerical Aperture Angle Calculator?

Definition: This calculator determines the half-angle of the light cone (θ) based on the numerical aperture (NA) and refractive index (n).

Purpose: It helps optical engineers and scientists understand the light-gathering capability of optical fibers and microscope objectives.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \theta \) — Half-angle of light cone (degrees)
• \( NA \) — Numerical aperture (dimensionless)
• \( n \) — Refractive index (dimensionless)

Explanation: The numerical aperture divided by the refractive index gives the sine of the acceptance angle, and the arcsine function converts this to an angle.

3. Importance of Numerical Aperture Angle

Details: The acceptance angle determines how much light can enter an optical system, affecting resolution and light-gathering capability.

4. Using the Calculator

Tips: Enter the numerical aperture (typically 0.1 to 1.0) and refractive index (1.0 for air, ~1.5 for glass). NA must be ≤ n.

5. Frequently Asked Questions (FAQ)

Q1: What is numerical aperture?
A: NA measures the light-gathering ability of an optical fiber or lens, defined as n·sinθ.

Q2: What are typical NA values?
A: For optical fibers: 0.1-0.3; microscope objectives: 0.1-1.4.

Q3: Why is refractive index important?
A: It affects how light bends when entering a medium, changing the maximum acceptance angle.

Q4: What if NA > n?
A: This is physically impossible as sinθ cannot exceed 1. The calculator will show no result.

Q5: How is this used in microscopy?
A: Higher NA and proper angles provide better resolution and light collection.