Question

The ratio of intensities at two points P and Q on the screen in a Young’s double slit experiment where phase difference between two wave of same amplitude are \(\frac{π}{3}\) and \(\frac{π}{2}\), respectively are 

• A. 3:2
• B. 2:3
• C. 1:3
• D. 3:1

Answer 1

The Correct Option is A

In a Young’s double slit experiment, the intensity at a point on the screen depends on the phase difference between the waves coming from the two slits. The resultant intensity \(I\) at a point is given by:

I = I_0 (1 + \cos \phi),

where I_0 is the maximum intensity (when the phase difference is zero) and \phi is the phase difference.

Let’s calculate the intensities at points P and Q where the phase differences are \frac{\pi}{3} and \frac{\pi}{2}, respectively.

1. For Point P:
   • Phase difference \phi_P = \frac{\pi}{3}
   • Intensity I_P = I_0 (1 + \cos \frac{\pi}{3})
   • Since \cos \frac{\pi}{3} = \frac{1}{2}, the intensity becomes:
   • I_P = I_0 (1 + \frac{1}{2}) = \frac{3I_0}{2}
2. For Point Q:
   • Phase difference \phi_Q = \frac{\pi}{2}
   • Intensity I_Q = I_0 (1 + \cos \frac{\pi}{2})
   • Since \cos \frac{\pi}{2} = 0, the intensity becomes:
   • I_Q = I_0 \cdot 1 = I_0

Finding the Ratio:

The ratio of intensities at points P and Q is:

\frac{I_P}{I_Q} = \frac{\frac{3I_0}{2}}{I_0} = \frac{3I_0}{2I_0} = \frac{3}{2}

Thus, the ratio of intensities at points P and Q is 3:2.

Conclusion: The correct option is 3:2.