An electromagnetic wave, whose wave normal makes an angle of 45^ with the vertical, travelling in air strikes a horizontal liquid surface. While travelling through the liquid it gets deviated through 15^ . What is the speed of the electromagnetic wave in the liquid, if the speed of electromagnetic wave in air is 3 10^8 ~m / s ? ( 30^ =0 5, 45^ = 1 2 )

Step-by-step solution

The angle of incidence is i =45^ The angle of deviation is =15^ The angle of refraction is aligned & =i-r & r=i- & r=45^ -15^ & r=30^ aligned The relation between the speed of the wave in the medium, the angle of incidence and the angle of refraction is given by the formula: aligned & v ₂ v ₁ = r i & v ₂ v ₁ = 30^ 45^ & v ₂ v ₁ = 1 2 aligned aligned & v ₂= v ₁ 2 & v ₂= 3 10^8 2 & v ₂=2.1 10^8 ~m / s aligned