Question

In Young's double slit experiment, the two equally bright slits are coherent, but of phase difference $\frac{\pi }{3}$. If maximum intensity on the screen is $I_o$, the intensity at the point on the screen equidistant from the slits is:

• A. $I_o$
• B. $\frac{I_o}{2}$
• C. $\frac{I_o}{4}$
• D. $\frac{3I_o}{4}$

Answer 1

The correct option is D $\frac{3I_o}{4}$

Given$:\varphi =\pi /3$

$I=I_{max}co{s}^2\left(\frac{\varphi }{2}\right)$

$I=I_{0}co{s}^2\left(\frac{\pi /3}{2}\right)$

$=I_{0}co{s}^2\left(\pi /6\right)$

$=I_0\left(\frac{\sqrt{3}}{2}{)}^2\right(\because cos\pi /6=\frac{\sqrt{3}}{2})$

$=I_0\frac{3}{4}$

So, intensity on the screen equidistant from the slats is $\frac{3}{4}{I}_0.$