The maximum distance upto which TV transmission from a TV tower of height h can be received is proportional to

Step-by-step solution

If the height of the antenna is h , then the maximum distance upto which the TV transmission for a TV tower can be received is proportional to h^ 1 / 2 . Suppose that the height of the TV antena be h and the radius of the earth be R and R>>h . Let A be a receiving station. In the limit h< < R , we can assume that B A is a tangent to the surface of the earth. Then B A O=90^ and so B O^2=A B^2+A O^2 (R+h)^2=A B^2+R^2 A B^2=R^2+h^2+2 R h-R^2=2 R h+h^2 as h< < R we neglect h^2 and so aligned & A B^2=2 R h A B= 2 R h &