Calculate the ratio of range of transmitting antenna of height 64 m to the receiving antenna of height 16 m:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2 : 1
The range of an antenna of height \( h \) is the distance to the horizon seen from its top. For the earth of radius \( R \),
\( \displaystyle d = \sqrt{2Rh} \;\Rightarrow\; d \propto \sqrt{h} \)
\( \displaystyle \frac{d_1}{d_2} = \sqrt{\frac{h_1}{h_2}} = \sqrt{\frac{64}{16}} = \sqrt{4} = 2 \)
So the ratio is \( 2 : 1 \).
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
\( \displaystyle d_T = \sqrt{2Rh_T} \)
where R is the radius of the earth (approximately 6400 km). dT is also called the radio horizon of the transmitting antenna.”