Q.A transmitting antenna at the top of a tower has a height 32 m and that of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in line of sight mode? Given radius of Earth is 6.4$\times$10$^6$ m.

Line-of-sight TV signals are limited by the curvature of the Earth; the range to the horizon from a tower of height $h$ is $d=\sqrt{2Rh}$.

TV signals (very high / ultra-high frequency) travel by line-of-sight propagation and are not reflected by the ionosphere, so their range is limited by the visible horizon from the transmitting tower. For a tower of height $h$ on a spherical Earth of radius $R$, geometry gives the maximum …

The line-of-sight range from a tower of height $h$ on the Earth (radius $R$) is $d_T = \sqrt{2Rh}$, giving $d_T = 8\sqrt{20}$ km here. Note: this topic (range of a transmitting antenna) belongs to the Communication Systems chapter, which is not in the current Haryana syllabus.

For a transmitting antenna/tower of height $h_T$ mounted on the (locally flat, curved) Earth of radius $R$, the maximum line-of-sight distance to the horizon is

$d_T = \sqrt{2Rh_T}$ …

Line-of-sight range from a tower of height $h$ on Earth of radius $R$ is $d=\sqrt{2Rh}$, from simple geometry.

Note: This question is from the Communication Systems chapter, which was removed from the current CBSE/Haryana Class-12 syllabus in the 2023 rationalisation. It is answered here for completeness since it appeared in this 2017 paper.

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