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Plane microwaves from a transmitter are directed normally towards a plane reflector. $A$ detector moves along the normal to the reflector. Between positions of $14$ successive maxima, the detector travels a distance $0.13\, m$. If the velocity of light is $3 \times 10^8 m/s$, find the frequency of the transmitter.
$1.5 \times 10^{10}\, Hz$
$10^{10}\, Hz$
$3 \times 10^{10} \,Hz$
$6 \times 10^{10}\, Hz$
Solution
The detector receives direct as well as reflected waves. The distance moved between two consecutive position of maxima is $\lambda / 2$
$14 \times \frac{\lambda}{2}=71=0.14 \mathrm{m}$
$\Rightarrow \lambda=0.02 m$
$c=n \lambda$
Putting $c=3 \times 10^{8} \mathrm{m} / \mathrm{s},$ we have
$n=\frac{c}{\lambda}=\frac{3 \times 10^{8}}{0.02}=1.5 \times 10^{10} \mathrm{Hz}$
