Question

In Young’s double slit experiment two disturbances arriving at a point P have phase difference of $\frac{\pi}{3}$.The intensity of this point expressed as a fraction of maximum intensity $I_{0}$is:

• A. $\frac{3}{2}I_{0}$
• B. $\frac{1}{2}I_{0}$
• C. $\frac{4}{3}I_{0}$
• D. $\frac{3}{4}I_{0}$

Answer 1

Answer: (D)

$\frac{3}{4}I_{0}$

Answer 2

: The resultant intensity

$I = I_{0}\cos^{2}\frac{\varphi}{2}$

Here, $I_{0}$is the maximum intensity and $\varphi = \frac{\pi}{3}$

$\therefore I = I_{0}\cos^{2}\left( \frac{\pi}{3 \times 2} \right) = I_{0}\cos^{2}\frac{\pi}{6} = I_{0}\left( \frac{\sqrt{3}}{2} \right)^{2}$

$I = \frac{3}{4}I_{0}$