In interference experiment the path difference between two interfering waves at a point A on the screen is /3 , where is the wavelength of these waves, and at another point B the path difference is /6 . The ratio of intensities at points A and B is _______.

Step-by-step solution

The phase difference is related to the path difference x by the relation = 2 x . For point A , the path difference is x_A = 3 . _A = 2 3 = 2 3 The intensity at point A is given by I_A = I_ max ^2 ( _A 2 ) . I_A = I_ max ^2 ( 3 ) = I_ max ( 1 2 )^2 = I_ max 4 For point B , the path difference is x_B = 6 . _B = 2 6 = 3 The intensity at point B is given by I_B = I_ max ^2 ( _B 2 ) . I_B = I_ max ^2 ( 6 ) = I_ max ( 3 2 )^2 = 3I_ max 4 The ratio of intensities at points A and B is: I_A I_B = I_ max 4 3I_ max 4 = 1 3 An