The correct formula for range of a transmitting antenna of height ‘2h’ is:
(Given R = radius of the Earth)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \sqrt{4Rh} \)
The range of a transmitting antenna of height \( h_T \) is the distance to the horizon, \( d_T = \sqrt{2Rh_T} \), where R is the radius of the earth. Here the height is \( 2h \).
\( d = \sqrt{2R\,(2h)} = \sqrt{4Rh} \)
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
Space Wave – “… If the transmitting antenna is at a height hT, then you can show that the distance to the horizon dT is given as \( d_T = \sqrt{2Rh_T} \), where R is the radius of the earth (approximately 6400 km). dT is also called the radio horizon of the transmitting antenna.”