Figure 33-61 depicts a simplistic optical fiber: a plastic core (n1=1.58) is surrounded by a pla

step 1 In this question, it is about total internal reflection in an optical fiber. So it contains a pl

Figure 33-61 depicts a simplistic optical fiber: a plastic...

Figure $33-61$ depicts a simplistic optical fiber: a plastic core $\left(n_{1}=1.58\right)$ is surrounded by a plastic sheath $\left(n_{2}=1.53\right) .$ A light ray is incident on one end of the fiber at angle $\theta .$ The ray is to undergo total internal reflection at point $\bar{A}$, where it encounters the core-sheath boundary. (Thus there is no loss of light through that boundary.) What is the maximum value of $\theta$ that allows total internal reflection at $\bar{A} ?$

Key Concepts

Index of Refraction

The index of refraction is a measure of how fast light travels within a material compared to its speed in a vacuum. It is crucial in determining how light rays bend when transitioning between different media and is a key parameter in analyzing light propagation through optical fibers.

Snell's Law

Snell's law defines the relationship between the angles of incidence and refraction when light passes through the boundary between two media with different refractive indices. This law is essential for determining how light rays are refracted as they enter or exit an optical fiber.

Critical Angle

The critical angle is the minimum angle of incidence beyond which light traveling from a medium with a higher refractive index to one with a lower refractive index is completely reflected rather than refracted. It is obtained from Snell's law by setting the angle of refraction to 90 degrees, and it underpins the phenomenon of total internal reflection.

Total Internal Reflection

Total internal reflection occurs when a light ray within a medium of higher refractive index strikes the interface with a medium of lower refractive index at an angle greater than the critical angle, resulting in all the light being reflected back into the original medium. This phenomenon is fundamental to the functioning of optical fibers.

Acceptance Angle in Optical Fibers

The acceptance angle is the maximum angle at which light can enter an optical fiber and still be guided along the core by total internal reflection. It is determined by the refractive indices of the core and the surrounding medium, ensuring that light rays are confined within the fiber for efficient signal transmission.

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