For distinct interference pattern to be observed, necessary condition is that ratio of intensity of light emission by both the sources should be :

Options

A. `2:1`
B. `1:2`
C. `1:1`
D. `1:4`

Answer

To solve the question regarding the necessary condition for distinct interference patterns to be observed, we can follow these steps:

### Step 1: Understand the Concept of Interference
Interference occurs when two or more coherent light sources overlap and combine their light waves. This results in a pattern of alternating bright and dark fringes known as interference fringes.

### Step 2: Define Intensity
Let the intensities of the two sources be \( I_1 \) and \( I_2 \). The intensity of light is proportional to the square of the amplitude of the light wave.

### Step 3: Determine Maximum and Minimum Intensities
The maximum intensity \( I_{\text{max}} \) and minimum intensity \( I_{\text{min}} \) in an interference pattern can be expressed as:
- \( I_{\text{max}} = (A_1 + A_2)^2 \)
- \( I_{\text{min}} = (A_1 - A_2)^2 \)

Where \( A_1 \) and \( A_2 \) are the amplitudes of the two sources related to their intensities by \( I_1 \propto A_1^2 \) and \( I_2 \propto A_2^2 \).

### Step 4: Calculate the Ratio of Intensities
The contrast of the interference pattern is determined by the ratio of maximum to minimum intensity:
\[ \text{Contrast} = \frac{I_{\text{max}}}{I_{\text{min}}} \]

Substituting the expressions for \( I_{\text{max}} \) and \( I_{\text{min}} \):
\[ \text{Contrast} = \frac{(A_1 + A_2)^2}{(A_1 - A_2)^2} \]

### Step 5: Condition for Distinct Interference Pattern
For the interference pattern to be distinctly observed, we want the contrast to be maximized. This occurs when the minimum intensity approaches zero, which happens when:
\[ A_1 - A_2 = 0 \quad \Rightarrow \quad A_1 = A_2 \]

This implies that the intensities must be equal:
\[ I_1 = I_2 \]

### Step 6: Conclusion
Thus, the necessary condition for distinct interference patterns to be observed is that the ratio of the intensities of the two sources should be:
\[ \frac{I_1}{I_2} = 1 \]

### Final Answer
The ratio of intensity of light emission by both sources should be 1:1.

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