### Correct Option: B. The minimum angle of incidence at which light is completely reflected within the fibre ### Detailed Explanation: **Understanding Total Internal Reflection:** Total internal reflection is a phenomenon that occurs when a light ray traveling in a denser medium (like glass or water) hits the boundary of a less dense medium (like air) at a certain angle. If the angle of incidence exceeds a specific threshold, known as the critical angle, the light will not pass into the less dense medium but will instead be completely reflected back into the denser medium. **Defining the Critical Angle:** The critical angle (\( \theta_c \)) can be mathematically defined using Snell's Law, which states: \[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \] Where: - \( n_1 \) is the refractive index of the denser medium (e.g., optical fibre), - \( n_2 \) is the refractive index of the less dense medium (e.g., air), - \( \theta_1 \) is the angle of incidence, - \( \theta_2 \) is the angle of refraction. At the critical angle, the angle of refraction (\( \theta_2 \)) becomes 90 degrees (the light travels along the boundary). Thus, we can rearrange Snell's Law to find the critical angle: \[ \sin(\theta_c) = \frac{n_2}{n_1} \] This means that the critical angle is the minimum angle of incidence at which light will be completely reflected within the optical fibre. **How It Affects Light Transmission:** In optical fibres, light is transmitted through total internal reflection. When light enters the fibre at an angle greater than the critical angle, it reflects off the walls of the fibre, allowing it to travel long distances with minimal loss. This is crucial for applications like telecommunications, where signals need to be transmitted over long distances without significant attenuation. ### Why Other Options Are Incorrect: - **Option A: The angle at which light can pass through the fibre without any reflection** - This option is incorrect because it describes the angle of incidence at which light can pass into the less dense medium, not the critical angle. The critical angle specifically refers to the angle beyond which light is reflected, not transmitted. - **Option C: The maximum angle at which light can enter the fibre without being lost** - This option is misleading. While it may seem related, the critical angle is not about the maximum angle for entering the fibre; rather, it is the minimum angle for total internal reflection. Light entering at angles less than the critical angle may be lost due to refraction. - **Option D: The angle at which light begins to refract outside the fibre** - This option is incorrect because it describes the behavior of light as it exits the fibre, not the critical angle. The critical angle is concerned with the conditions under which light is reflected back into the fibre, not when it refracts out. ### Summary of Key Points: - The critical angle is the minimum angle of incidence for total internal reflection in optical fibres. - It is determined by the refractive indices of the two media involved. - Light transmitted through optical fibres relies on total internal reflection to minimize loss. - Understanding the critical angle is essential for optimizing light transmission in fibre optics. This thorough understanding of the critical angle and its implications in optical fibres is crucial for anyone studying physics, especially in the context of optics and telecommunications.