Question

The intensity of the primary maximum in a two-slit interference pattern is given by \(I_2\), and the intensity of the primary maximum in a three-slit interference pattern is given by \(I_3\). Assuming the far-field approximation, same slit parameters, and same incident light intensity in both cases, \(I_2\) and \(I_3\) are related as:

• A. \(I_2 = \dfrac{3}{2} I_3\)
• B. \(I_2 = \dfrac{9}{4} I_3\)
• C. \(I_2 = \dfrac{2}{3} I_3\)
• D. \(I_2 = \dfrac{4}{9} I_3\)

Hint:

In multi-slit interference, intensity at the central maximum increases as the square of the number of slits (\(I \propto n^2\)).

Answer 1

The Correct Option is D

Step 1: Recall formula for interference maxima.
For \(n\) slits, the intensity of the primary maximum is proportional to \(n^2\), i.e., \[ I_n \propto n^2 \]

Step 2: Take ratio for two and three slits.
\[ \frac{I_2}{I_3} = \frac{2^2}{3^2} = \frac{4}{9} \]

Step 3: Conclusion.
Hence, \(I_2 = \dfrac{4}{9} I_3\).