In Young's Double Slit Experiment (YDSE), the superposition principle determines the intensity of maxima and minima. When two light waves with intensities \( I_1 \) and \( I_2 \) interfere, the maximum and minimum intensities are calculated as follows:
- Maximum intensity: \( I_{\text{max}} = I_1 + I_2 \)
- Minimum intensity: \( I_{\text{min}} = |I_1 - I_2| \)
For the specified problem:
- \( I_1 = 4I \)
- \( I_2 = 9I \)
Consequently, the maximum intensity is \( 4I + 9I = 13I \), and the minimum intensity is \( |4I - 9I| = 5I \).
The difference between the maximum and minimum intensity is:
\[
\Delta I = 13I - 5I = 8I
\]
Therefore, the difference is \( 8I \).