Figure 33-45 depicts a simplistic optical fiber: a plastic core (n1=1.58) is surrounded by a pla

step 1 Hello everyone here, theta i is equal to theta c, so sine theta i is equal to sine theta c, that

Figure 33-45 depicts a simplistic optical fiber: a plastic...

Figure 33-45 depicts a simplistic optical fiber: a plastic core $\left(n_{1}=1.58\right)$ is surrounded by a plastic sheath $\left(n_{2}=1.46\right)$. A light ray is incident on one end of the fiber at angle $\theta$. The ray is to undergo total internal reflection at point $A$, where it encounters the core-sheath boundary. (Thus there is no loss of light through that bound- ary.) What is the maximum value of $\theta$ that allows total internal reflection at $A$ ?

Figure 33-45 depicts a simplistic optical fiber: a plastic core $\left(n_{1}=1.58\right)$ is surrounded by a plastic sheath $\left(n_{2}=1.46\right)$. A light ray is incident on one end of the fiber at angle $\theta$. The ray is to undergo total internal reflection at point $A$, where it encounters the core-sheath boundary. (Thus there is no loss of light through that bound-
ary.) What is the maximum value of $\theta$ that allows total internal reflection at $A$ ?

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Key Concepts

Total Internal Reflection

A phenomenon in optics where light, traveling in a medium with a higher refractive index, is completely reflected at the boundary with a medium of lower refractive index when the incidence angle exceeds a specific value. This is the principle that allows optical fibers to transmit light with minimal loss.

Critical Angle

The minimum angle of incidence relative to the normal at which total internal reflection occurs. It is determined by the refractive indices of the two media at the interface using Snell's law, and is essential in ensuring that light is confined within the optical fiber.

Snell's Law

A fundamental law of refraction stating that the product of the refractive index and the sine of the angle of incidence is constant across an interface. It is used to derive the critical angle needed for total internal reflection in optical fibers.

Acceptance Angle

The maximum angle at which light can enter an optical fiber and still be guided by total internal reflection. This concept is closely related to the numerical aperture of the fiber and determines the range of incoming light directions that will propagate along the fiber.

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