Question

Light from two coherent sources of the same amplitude $A$ and wavelength $\lambda$ illuminates the screen. The intensity of the central maximum is $I_0$. If the sources were incoherent, the intensity at the same point will be.

• A. $4I_0$
• B. $1I_0$
• C. $I_0$
• D. $\frac{I_0}{2}$

Answer 1

Answer: (D)

$\frac{I_0}{2}$

For two coherent sources, $I_1=I_2=I$
$I_C=(\sqrt{I_1}+\sqrt{I_2}{)}^2=I+I+2Icos\theta$
This is given as $I_0$ for maximum for $cos\theta =1$
So, $I_0=I_{Cmax}=2I+2I=4I$
Hence, $I=\frac{I_0}{4}$-----------(1)
Now, when the sources will be incoherent, then:
$I_{incmax}=I+I=2I$-----(2)
From equation (1) and (2):
$I_{incmax}=2\times \frac{I_0}{4}$
$\Rightarrow I_{incmax}=\frac{I_0}{2}$
Hence, the correct option is $\left(D\right)$