Q: A flood light is covered with a filter that transmits red light . The electric field of the emerging beam is represented by a sinusoidal plane wave $\large E_x = 36 sin(1.2 \times 10^7 z – 3.6 \times 10^{15} t ) V/m $ .The average intensity of beam in watt/m^{2} will be

(a) 6.88

(b) 3.44

(c) 1.72

(d) 0.86

Sol: Average Intensity ,

$\large I_{av} = \frac{1}{2}\epsilon_0 E_0^2 c $

$\large I_{av} = \frac{8.85 \times 10^{-12}\times (36)^2 \times (3 \times 10^8)}{2} $

= 1.72 W/m^{2}