For the optical fiber shown in the figure, find the minimum angle of incidence (θi) that will result in total internal reflection if the refractive index for the cladding (n2) is 1.42 and the refractive index of the core is (A.) n1=1.55 and (B.) n1=1.69.

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For the optical fiber shown in the figure, find the minimum angle of incidence (θi) that will result in total internal reflection if the refractive index for the cladding (n2) is 1.42 and the refractive index of the core is (A.) n1=1.55 and (B.) n1=1.69.

The image illustrates the concept of light transmission through an optical fiber, focusing on the cone of acceptance and total internal reflection. 

### Diagram Breakdown:

1. **Cone of Acceptance:**
   - The orange shaded area represents the "cone of acceptance," which is the range of angles within which light can enter the optical fiber and be successfully transmitted. 
   - The angle of incidence, denoted as \( \theta_i \), is the angle at which light enters the fiber.

2. **Optical Fiber Structure:**
   - The fiber consists of two main parts: 
     - **Core** (center region with refractive index \( n_1 \)): This is where the light is transmitted.
     - **Cladding** (outer layer with refractive index \( n_2 \)): It surrounds the core and has a lower refractive index, allowing for total internal reflection.

3. **Light Propagation:**
   - The green arrows depict the path of light as it enters and travels through the core.
   - When light hits the boundary between the core and cladding, it is reflected internally because \( n_1 > n_2 \).
   - The angle of reflection, \( \theta_r \), is shown in relation to the angle of incidence.

### Explanation:

In optical fibers, light is guided through the core by repeated total internal reflections due to the difference in refractive indices between the core and cladding. The cone of acceptance defines the range of angles that allow light to be properly transmitted through the fiber without loss. This principle is essential for efficient data transmission in telecommunications and networking applications.
Transcribed Image Text:The image illustrates the concept of light transmission through an optical fiber, focusing on the cone of acceptance and total internal reflection. ### Diagram Breakdown: 1. **Cone of Acceptance:** - The orange shaded area represents the "cone of acceptance," which is the range of angles within which light can enter the optical fiber and be successfully transmitted. - The angle of incidence, denoted as \( \theta_i \), is the angle at which light enters the fiber. 2. **Optical Fiber Structure:** - The fiber consists of two main parts: - **Core** (center region with refractive index \( n_1 \)): This is where the light is transmitted. - **Cladding** (outer layer with refractive index \( n_2 \)): It surrounds the core and has a lower refractive index, allowing for total internal reflection. 3. **Light Propagation:** - The green arrows depict the path of light as it enters and travels through the core. - When light hits the boundary between the core and cladding, it is reflected internally because \( n_1 > n_2 \). - The angle of reflection, \( \theta_r \), is shown in relation to the angle of incidence. ### Explanation: In optical fibers, light is guided through the core by repeated total internal reflections due to the difference in refractive indices between the core and cladding. The cone of acceptance defines the range of angles that allow light to be properly transmitted through the fiber without loss. This principle is essential for efficient data transmission in telecommunications and networking applications.
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