In a Young's double slit set up using monochromatic light of wavelength `lambda` the intensity of light at a point, where path difference is `2lambda` is found to be `I_(0)` What will be the intensity at a point when path different is `lambda//3` ?

Explanation

To solve the problem, we need to find the intensity of light at a point where the path difference is \(\frac{\lambda}{3}\) in a Young's double slit experiment, given that the intensity at a path difference of \(2\lambda\) is \(I_0\).

### Step-by-Step Solution:

1. **Understanding the Relationship Between Intensity and Phase Difference**:
The intensity \(I\) at any point in a Young's double slit experiment can be expressed in terms of the maximum intensity \(I_0\) and the phase difference \(\phi\) as:
\[
I = I_0 \cos^2\left(\frac{\phi}{2}\right)
...