Question

If \(\mathrm{M}_{1} \& \mathrm{M}_{2}\) are the refractive indices of the material of core and cladding of an optical fiber, than the loss of light due to its leakage can be minimized by having (A) \(\mathrm{M}_{1}>\mathrm{M}_{2}\) (B) \(\mathrm{M}_{1}<\mathrm{M}_{2}\) (C) \(\mathrm{M}_{1}=\mathrm{M}_{2}\) (D) None of these

Short answer

The loss of light due to leakage in an optical fiber can be minimized by having the refractive index of the core (M1) greater than the refractive index of the cladding (M2). This condition ensures total internal reflection within the core and minimizes light leakage. Therefore, the correct answer is: (A) M1 > M2

Step-by-step solution

Recall the condition for total internal reflection (TIR)

Total internal reflection occurs when a light wave travels from a medium with a higher refractive index (M1) to a medium with a lower refractive index (M2) and the angle of incidence is greater than the critical angle. The critical angle is given by the formula: \[ \theta_c = \sin^{-1} \left(\frac{M2}{M1}\right) \] Where θc is the critical angle, M1 is the refractive index of the core, and M2 is the refractive index of the cladding.

Determine the condition for minimizing light leakage

To minimize the loss of light due to leakage, the total internal reflection must be ensured inside the optical fiber. Based on the TIR condition, this can be achieved when: 1. The refractive index of the core (M1) is greater than the refractive index of the cladding (M2). 2. The angle of incidence is greater than the critical angle. From the choices given, the correct answer is: (A) M1 > M2 This condition ensures that the light will undergo total internal reflection within the core and minimize the loss of light due to leakage into the cladding.

Key concepts

Refractive Index

The refractive index, often symbolized as "n," is a measure of how much the speed of light is reduced inside a medium, compared to the speed of light in a vacuum. It is a crucial concept in optics, influencing how light propagates through different materials. The refractive index formula is:\[n = \frac{c}{v}\]Here, "c" represents the speed of light in a vacuum, which is approximately 299,792,458 meters per second, and "v" is the speed of light in the medium. Understanding refractive index helps in predicting how light behaves when it encounters a boundary between two materials with different refractive indices. If light travels from a medium with a high refractive index to a lower one, it bends away from the normal. This bending of light is attributed to the difference in velocity caused by the varying densities of the mediums. In summary, the refractive index tells us about the optical density of materials and plays a vital role in mechanisms like refraction and total internal reflection within optical systems such as lenses, microscopes, and optical fibers.

Critical Angle

The critical angle is a specific angle of incidence at which light passing from a medium with a higher refractive index to a lower refractive index medium is refracted along the boundary, rather than passing through. At this angle, the refracted ray travels along the boundary and the angle of refraction becomes 90 degrees.The critical angle \(\theta_c\) is determined by using the formula:\[\theta_c = \sin^{-1} \left(\frac{n_{2}}{n_{1}}\right)\]where \(n_1\) and \(n_2\) are the refractive indices of the two media, with \(n_1 > n_2\).

• If the angle of incidence is greater than the critical angle, total internal reflection occurs. This means the light is completely reflected back into the original medium, a principle used in various optical devices such as fiber optics.
• If the incident angle is less than the critical angle, the light is simply refracted from one medium to another.

The concept of the critical angle is instrumental in designing devices where control over light propagation is necessary, ensuring efficient travel through mediums with minimal loss.

Optical Fiber

Optical fibers are thin, flexible strands of glass or plastic that are capable of transmitting light signals over long distances. They exploit the principle of total internal reflection to carry these light signals with minimal loss. At the core of an optical fiber are two layers: a central core and a surrounding cladding.

• The core is the inner part where light travels, typically having a higher refractive index.
• The cladding around it has a slightly lower refractive index, allowing light to remain trapped within the core.

When light is introduced into the core, it strikes the boundary at an angle greater than the critical angle, leading to total internal reflection. This keeps the light bouncing down the fiber, even if it bends, ensuring efficient transmission. Optical fibers are crucial in modern telecommunications, enabling high-speed internet, cable TV, and telephone services, thanks to their ability to carry large quantities of data over long distances without signal degradation. They are also used in medical instruments and image capture devices, demonstrating the versatile nature of light manipulation within optical fibers.