Question

If ratio of intensity of light from two sources are 1 : 9 then find the resultant intensity ratio if sources are coherent with phase difference is 60° in one case and incoherent in the other case

(1) 1 : 1

(2) 10 : 13

(3) 13 : 10

(4) 26 : 13

Answer 1

Correct option is (3) 13 : 10

\(I_{re} = I_1 + I_2 + 2\sqrt{I_1I_2} \cos \Delta \phi\)

\(I_{re} = I + 9I + 2\sqrt{9I^2} \times \frac 12\) 

\(I_{re} = 13I\)

For Incoherence

\(I_n = I_1 + I_2\)

\(I_n = 10I\) 

\(\frac{I_{re}}{I_{n}} = \frac {13}{10}\)