The impedance matching Network shown in figure is to match a lossless line having characteristic impedance $Z_o= 50 \Omega$ with a load impedance $Z_L$. A quarter - Wave line having a characteristic impedance $Z_1=75 \Omega$ is connected to $Z_L$. Two stubs having characteristic impedance of $75 \Omega$ each are connected to this quarter - wave line. One is a short - circuited (S.C) stub of length $0.25 \lambda$ connected across PQ and the other one in an open - Circuted (O.C) stub of length 0.5 $\lambda$ connected across RS.

The impedance matching is achieved when the real part of $Z_L$ is

The refractive indices of the core and cladding of an optical fiber are 1.50 and 1.48 respectively. The critical propagation angle. Which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is $\_\_\_\_$ degree.

An antenna with a directive gain of 6 dB is radiating a total power of 16 kw . The amplitude of the electric field in free space at a distance of 8 km from the antenna in the direction of 6 dB gain(rounded off to three decimal places is$\_\_\_\_$ $\mathrm{V} / \mathrm{m}$.

A standard air-filled rectangular waveguide with dimensions $a=8 \mathrm{~cm}, b=4 \mathrm{~cm}$, operates at 3.4 GHz . For the dominant mode of wave propagation, the phase velocity of the signal is $v_p$. The value (rounded off to two decimal places) of $v_p / c$, where $c$ denotes the velocity of light, is $\_\_\_\_$ .