A radar has power of 1 kW and is operating at a frequency of 10 GHz. It is located on a mountai

step 1 Hi friends, maximum distance on the earth where object can be detected, H plus R whole square eq

A radar has power of 1 kW and is operating at a frequency...

A radar has power of $1 \mathrm{~kW}$ and is operating at a frequency of $10 \mathrm{GHz}$. It is located on a mountain top of height $500 \mathrm{~m}$. The maximum distance up to which it can detect object located on the surface of the earth (Radius of earth $=6.4 \times 10^{6} \mathrm{~m}$ ) is (A) $16 \mathrm{~km}$ (B) $40 \mathrm{~km}$ (C) $64 \mathrm{~km}$ (D) $80 \mathrm{~km}$

A radar has power of $1 \mathrm{~kW}$ and is operating at a frequency of $10 \mathrm{GHz}$. It is located on a mountain top of height $500 \mathrm{~m}$. The maximum distance up to which it can detect object located on the surface of the earth (Radius of earth $=6.4 \times 10^{6} \mathrm{~m}$ ) is
(A) $16 \mathrm{~km}$
(B) $40 \mathrm{~km}$
(C) $64 \mathrm{~km}$
(D) $80 \mathrm{~km}$

Key Concepts

Effects of Earth's Curvature

The Earth's curvature plays a significant role in limiting the range of systems that rely on direct line-of-sight propagation, such as radar. Because the Earth is curved, objects that are too far away eventually fall below the horizon, making them undetectable regardless of the system's power or frequency. Understanding this concept is important in areas ranging from radio signal propagation to navigation and remote sensing.

Line-of-Sight (LOS) Distance

This refers to the maximum distance at which an observer or sensor can directly 'see' an object without any obstruction. In contexts such as radar detection, the LOS distance is crucial because the curvature of the Earth can block the view of objects beyond the geometric horizon. The concept is based on simple geometric relationships and is fundamental in many fields including communications, aviation, and radar technology.

Geometric Horizon Calculation

Geometric horizon calculation is a method to determine the distance to the horizon from a given elevation. Using the formula d = ?(2Rh), where R is the radius of the Earth and h is the height above the Earth's surface, one can compute the distance at which the Earth's curvature starts to hide the surface. This calculation is essential when evaluating the maximum range for devices like radars and other line-of-sight systems.

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