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} $ .



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