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Calculate the angle of refraction at the air/core interface, r . critical angle, c and incident angle at the core/cladding interface, i . Will this light ray propagate down the fiber? You have the following data: nair = 1, ncore = 1.46, ncladding =1.43, incident =12o Answers: r = 8.2o , c = 78.4o , i = 81.8o light will propagate

### Formula Summary

**Index of Refraction:**
\[ n = \frac{c}{v} \]

**Snell’s Law:**
\[ n_1 \sin \theta_1 = n_2 \sin \theta_2 \]

**Critical Angle:**
\[ \theta_c = \sin^{-1} \left(\frac{n_2}{n_1}\right) \]

**Acceptance Angle:**
\[ \alpha = \sin^{-1} \left(\sqrt{n_1^2 - n_2^2}\right) \]

**Numerical Aperture:**
\[ NA = \sin \alpha = \sqrt{n_1^2 - n_2^2} \]

### Explanation

- The **Index of Refraction** (\( n \)) is the ratio of the speed of light in a vacuum (\( c \)) to the speed of light in a medium (\( v \)).

- **Snell's Law** relates the angles of incidence (\( \theta_1 \)) and refraction (\( \theta_2 \)) to the refractive indices of two different media (\( n_1 \) and \( n_2 \)).

- The **Critical Angle** (\( \theta_c \)) is the angle of incidence above which total internal reflection occurs, calculated using the refractive indices.

- The **Acceptance Angle** (\( \alpha \)) is the maximum angle at which light can enter a fiber optics cable and still be guided, calculated by the difference in refractive indices.

- **Numerical Aperture** (\( NA \)) is a measure of the light-gathering ability of an optical fiber, determined by the acceptance angle.

This summary provides key formulas relevant to optical physics, specifically focusing on light propagation and refraction principles.

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