Answer to Question #200376 in Optics for Piolo

Question

Components of some computers communicate with each other through optical fibers having an index of refraction n = 1.547. What time (in ns) is required for a signal to travel 0.142 m through such a fiber?

answer to 3 decimal places

Answer 1

• The principle
• If we know the refractive index of the fiber optics, the speed of light traveling through the fiber optic can be calculated.
• Note that the refractive index of a material is the relative speed of light traveling in that material compared to the speed of light traveling in a vacuum given by the formula
• n=c/v --------------------------------------------------------------------------------------------------------------------------1
• in which n is the refractive index of a material, c is the light speed in a vacuum and v is the light speed in the material.
• Therefore, since we know the refractive index of the material (n) and the speed of light in a vacuum, (c) we can calculate the speed of light by using the formula
• v=c/n---------------------------------------------------------------------------------------------------------------------------2
• Once we know the velocity of light in the fiber optical cable from the equation above, and we know the distance over which the light will travel, the duration of light travel can be calculated by using the velocity equation
• v=d/t---------------------------------------------------------------------------------------------------------------------------3
• Hence, the time taken for light to travel through the distance d once speed in the material is known can be given by
• t=d/v---------------------------------------------------------------------------------------------------------------------------4
• In our case, the refractive index of the fiber optic is n=1.547
• Speed of light in a vacuum is a constant at 3x10^8 m/s
• The speed of light in the fiber optics will be given by equation 2:
• v=3x10^8/1.547 = 1.939x10^8m/s
• Since we have the speed of light in the fiber optics and the distance d, we can calculate the duration it would take for light to travel through this distance using equation 3.
• t=0.142/1.939x10^8 = 7.322x10^-10 s
• Converting 7.322x10^-1seconds to nanoseconds gives 7322466667.000 ns