What is the maximum usable frequency for an E-layer of an ionosphere having critical frequency 4 MHz when the angle of incidence is $60^{\circ}$?
A. 5 MHz
B. 6 MHz
C. 8 MHz
D. 9 MHz

Hint:The ionosphere is a layer of electrons and electrically charged atoms and molecules that covers the Earth and stretches from about 50 kilometres (31 miles) to over 1,000 kilometres (620 mi). It occurs largely as a result of the Sun's ultraviolet radiation.

Complete step by step answer:
The maximum accessible frequency (MUF) in radio transmission is the highest radio frequency that can be used for transmission between two points through ionosphere reflection (skywave or "skip" propagation) at a given time, regardless of transmitter capacity.In the case of shortwave broadcasts, this index is particularly helpful.

A main mode of long-distance propagation in shortwave radio transmission is for radio waves to bounce off the ionised layers of the atmosphere and return diagonally to Earth. This allows radio waves to pass above the horizon and across the Earth's curve.

"Frequencies below 10 MHz are usually reflected at occurrence, but active events may cause frequencies up to 50 MHz and higher to be reflected by the E-layer." The optimum operating frequency for a given route is usually determined to be 80 to 90% of the MUF.

The MUF is about 3 times the critical frequency as a rule of thumb. where \[\theta \] is the angle of incidence and the critical frequency is the peak frequency reflected for a pulse propagating directly upward.
\[\text{Maximum Usable frequency}= \dfrac{\text{critical frequency}}{{\cos \theta }}\]
Here \[\theta \] is the angle of incidence.
\[MUF = \dfrac{4}{{\cos {{60}^o}}} \\
\Rightarrow MUF = \dfrac{4}{{\dfrac{1}{2}}} \\
\therefore MUF = 8\]

Note:The maximum amplitude of frequency at which waves enter the ionosphere and below which waves are reflected out from the ionosphere is known as critical frequency.Its value is not set and is determined by the ionosphere's electron density.