(i) The intensity of a light pulse travelling along a communication channel decreases exponentially with distance x according to the relation I = I_{o}e^{–αx}, where I_{o} 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 log_{10}(I/I_{0}) . 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?