Consider a step-index multimode fiber with NA = 0.2, n₁ = 1.5, a fiber = 0.6 dB-km-¹, and r = 50ns.

(a) Using the results of the previous problem, calculate the ratio of the back scattered power tothe input power for t₁ = 0 (i.e., for light back scattered from the segment of the fiber located right at the input of the test fiber).

(b) Calculate the ratio of the back scattered power to the input power for a segment of fiber located 10 km from the input of the fiber.

(c) Calculate the ratio of the back scattered power from the segment located 10 km from the input to the back scattered power from the segment located right in front of the input.

(d) The dynamic range, DR, (in dB) of an OTDR is defined as \mathrm{DR}=10 \log \left(\frac{P_{\mathrm{s} \max }}{P_{\mathrm{s} \min }}\right) where P max is the power of the strongest back scattered signal that can be detected at the OTDR receiver and Ps min is the power of the weakest signal that can be detected. If the dynamic range of the detector is 20 dB, calculate the maximum operating range of the OTDR,assuming that fiber loss is the only loss encountered (i.e., there are no connector or splice losses). You may assume that the coupler that connects the laser to the OTDR fiber pigtail(and the detector to the pigtail) has a 3 dB loss for each pass through it.