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(i) The intensity of a light pulse travelling along a communication channel decreases exponentially with distance x according to the relation I = Ioe–αx, where Io is the intensity at x = 0 and α is the attenuation constant. 

Show that the intensity reduces by 75 per cent after a distance of(In 4/α)

(ii) Attenuation of a signal can be expressed in decibel (dB) according to the relation dB =10 log10(I/I0) . What is the attenuation in dB/km for an optical fibre in which the intensity falls by 50 per cent over a distance of 50 km?

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(ii) 10log10 I/Io=-αx where α is the attenuation in dB/km.

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