We know that an electromagnetic wave is produced by periodically changing electric field (by an accelerating charged particle). We know that the electric field of a point charge varies inversely with square of distance from the charge. Therefore the amplitude of the electromagnetic wave such as light must go on decreasing and practically vanish on covering a finite distance. But , as we know, it doesn't happen and we see the light waves coming from stars very far away. Then what's happening there? Or am I wrong? Please explain.
The reason we can see stars from far away is because those stars are unimaginably bright up close. Stars do vary in brightness depending on the star type and distance, and there are certainly stars whose light we cannot see. Read about apparent magnitude and absolute magnitude.