Question

The two coherent sources produce interference with intensity ratio 'b'. In the interference pattern, the ratio \[ \frac{I_{\text{max}}}{I_{\text{min}}} \] will be

• A. \( 1 + b \)
• B. \( \frac{b}{1 + b} \)
• C. \( 2b \)
• D. \( \frac{1 + b}{b} \)

Hint:

In interference patterns, the intensity ratio is determined by the square of the amplitude ratio, which depends on the phase difference between the waves.

Answer 1

The Correct Option is D

Step 1: Understanding the problem.
The problem involves two coherent sources that produce interference, and the intensity ratio between the maxima and minima is given as \( b \). We are asked to find the ratio \( \frac{I_{\text{max}}}{I_{\text{min}}} \), where \( I_{\text{max}} \) is the maximum intensity and \( I_{\text{min}} \) is the minimum intensity.

Step 2: Intensity in interference.
In interference patterns, the maximum and minimum intensities are related to the amplitude of the waves. The intensity \( I \) is proportional to the square of the amplitude \( A \), so we can write:
\[ I_{\text{max}} = (A_{\text{max}})^2, \quad I_{\text{min}} = (A_{\text{min}})^2. \]
The intensity ratio is the square of the ratio of the amplitudes.

Step 3: Relationship between amplitudes.
The relationship between the amplitudes of the two waves at the maximum and minimum points is given by:
\[ A_{\text{max}} = \sqrt{1 + b}, \quad A_{\text{min}} = \sqrt{1 - b}. \]

Step 4: Finding the intensity ratio.
The intensity ratio is:
\[ \frac{I_{\text{max}}}{I_{\text{min}}} = \frac{(A_{\text{max}})^2}{(A_{\text{min}})^2} = \frac{1 + b}{b}. \]
Final Answer:
Thus, the ratio \( \frac{I_{\text{max}}}{I_{\text{min}}} \) is:
\[ \boxed{\frac{1 + b}{b}}. \]