Optics Question 152
Question: In Young’s double slit experiment, the two slits act as coherent sources of equal amplitude A and wavelengthl. In another experiment with the same set up the two slits are of equal amplitude A and wavelength l but are incoherent. The ratio of the intensity of light at the mid-point of the screen in the first case to that in the second case is
[IIT-JEE 1986; RPMT 2002]
Options:
A) 1 : 2
B) 2 : 1
C) 4 : 1
D) 1 : 1
Show Answer
Answer:
Correct Answer: B
Solution:
Resultant intensity $ I=I _{1}+I _{2}+2\sqrt{I _{1}I _{2}}\cos \varphi $
At central position with coherent source (and $ I _{1}=I _{2}=I _{0} $
$ I _{con}=4I _{0} $ … (i)
In case of incoherent at a given point, f varies randomly with time so (cos f)av = 0 \ $ {I _{Incoh}}=I _{1}+I _{2}=2I _{0} $ … (ii)
Hence $ \frac{I _{coh}}{I _{Incoh}}=\frac{2}{1} $ .
