The maximum distance a up to which T.V transmission from a...

The maximum distance a up to which T.V transmission from a T.V. tower of height $h$ can be received is Proportional to
(A) $\mathrm{h}^{(1 / 2)}$
(B) $\mathrm{h}$
(C) $\mathrm{h}^{(3 / 2)}$
(D) $\mathrm{h}^{2}$

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Key Concepts

Line-of-Sight Propagation

This concept explains how electromagnetic signals travel in straight lines and are limited by obstacles, such as the curvature of the Earth. The radio horizon is defined by where the line-of-sight tangentially meets the Earth, thus determining how far a signal can be received.

Horizon Distance Calculation

This involves the geometric relationship used to estimate the distance to the horizon, typically resulting in a formula where the distance is proportional to the square root of the height of the transmitting antenna. This relationship is derived from the properties of a circle (representing Earth) and tangential lines drawn from the antenna.

Proportional Relationships in Physics

Understanding proportionality is key to analyzing how one physical quantity scales with another. In this context, recognizing that the distance a signal travels scales with the square root of the height helps in interpreting and predicting transmission ranges based on changes in antenna elevation.

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