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(i) The intensity of a light pulse trave...

(i) The intensity of a light pulse travelling along a communication channel decreases exponentially with distance x according to the relation `I = I_0 e^(-alphax)`, where `I_0` is the intensity at ` x = 0 ` and `alpha` is the attenuation constant.
Show that the intensity reduces by 75 percent after a distance of `(ln 4)/(alpha)`
(ii) Attenuation of a signal can be expressed in decibel (dB) according to the relation
dB `= 10log_10 (I//I_0).` What is the attenuation in `dB//km` for an optical fibre in which the intensity falls by 50 percent over a distance of 50 km?

A

0.7

B

0.75

C

0.8

D

0.85

Text Solution

Verified by Experts

The correct Answer is:
B
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