Question

What is the ratio of critical frequency for reflection of radio waves from E, F1 and F2 layers in ionosphere if the electron densities are \[2 \times {10^{11}}\], \[3 \times {10^{11}}\] and \[8 \times {10^{11}}\]\[{m^{ - 3}}\] respectively?
A. 1: 2: 3
B. 1: 1.5: 3
C. 1.41: 1.73: 2.83
D. 1.52: 1.52: 1.89

Answer 1

Hint: To find the correct option for this question we will use the formula that relates the electron density with critical frequency. We take: \[{v_c} = 9\sqrt {{N_{\max }}} \] where \[{v_c}\] is the critical frequency and \[{N_{\max }}\] is the maximum electron density of a layer in the ionosphere. We will calculate the critical frequency for each layer with the help of given data and then evaluate the required frequency ratio of the radio waves from $E$, $F_1$ and $F_2$ layers.

Complete step by step answer:
To get the correct answer to this Formula used: \[{v_c} = 9\sqrt {{N_{\max }}} \] where \[{v_c}\]is the critical frequency and \[{N_{\max }}\]is the maximum electron density of a layer in the ionosphere.
Step I
Calculating critical frequencies for E, F1 and F2 layers
Let \[{v_E},{v_1}\]and \[{v_2}\]are the critical frequencies for E, F1 and F2 layers respectively.
Given:
\[{N_E} = 2 \times {10^{11}}{m^{ - 3}}\]
\[{N_1} = 3 \times {10^{11}}{m^{ - 3}}\] and
\[{N_2} = 8 \times {10^{11}}{m^{ - 3}}\]
So, \[{v_E} = 9\sqrt {2 \times {{10}^{11}}} \]…….(i)
\[{v_1} = 9\sqrt {3 \times {{10}^{11}}} \]…………… (ii)
\[{v_2} = 9\sqrt {8 \times {{10}^{11}}} \]…………. (iii)

Step II
Calculating the ratio of critical frequencies
Taking the ratio of eqn (i), eqn (ii),and eqn (iii), we get\[ \Rightarrow {v_E}:{v_1}:{v_2} = \sqrt 2 :\sqrt 3 :\sqrt 8 \]
\[{v_E}:{v_1}:{v_2} = 9\sqrt {2 \times {{10}^{11}}} :9\sqrt {3 \times {{10}^{11}}} :9\sqrt {8 \times {{10}^{11}}} \]

So, \[{v_E}:{v_1}:{v_2} = 1.41:1.73:2.83\]

$\therefore $ The ratio of critical frequency for reflection of radio waves from $E$,$ F_1$ and $F_2$ layers is \[{v_E}:{v_1}:{v_2} = 1.41:1.73:2.83\]. Hence, Option (C) is the correct answer.

Note:
Students must have an understanding of how the reflection of radio waves occurs from different layers of the ionosphere and the measure factors that affect the reflection phenomenon over there. One should also learn how the ionic sphere helps to make the communication from one place to another place through a long radio wave possible. In order to master these kinds of problems, the key is to keep practicing a lot of formula-based questions on this topic. Students must revise all the important results of derivations and their practical applications around us. We should also make some formula based short notes to such types of direct formula based tackle problems.