In the Young's double slit experiment, the interference pattern is found to have as intensity ratio between the bright and dark fringes as 9. This implies that

Options

A. the intensities at the screen due to the two slits are 5 units and 4 units respectively.
B. the intensities at the screen due to the two slits are 4 units and 1 units respectively.
C. the amplitude ratio is 3.
D. the amplitude ratio is 2.

Answer

To solve the problem regarding the intensity ratio between the bright and dark fringes in Young's double slit experiment, we can follow these steps:

### Step 1: Understand the given intensity ratio
We are given that the intensity ratio between the bright and dark fringes is 9:1. This means that if we denote the maximum intensity (I_max) as \( I_1 \) and the minimum intensity (I_min) as \( I_2 \), we can write:
\[ \frac{I_1}{I_2} = 9 \]

### Step 2: Relate intensity to amplitudes
In wave optics, the intensity (I) is proportional to the square of the amplitude (A). Therefore, we can express the intensities in terms of amplitudes:
\[ I_1 \propto A_1^2 \quad \text{and} \quad I_2 \propto A_2^2 \]
Thus, we can write the ratio of intensities as:
\[ \frac{I_1}{I_2} = \frac{A_1^2}{A_2^2} \]

### Step 3: Substitute the intensity ratio into the amplitude ratio
From the intensity ratio \( \frac{I_1}{I_2} = 9 \), we can write:
\[ \frac{A_1^2}{A_2^2} = 9 \]
Taking the square root of both sides gives:
\[ \frac{A_1}{A_2} = 3 \]
This indicates that the amplitude ratio is 3:1.

### Step 4: Calculate the individual intensities
Since we know the ratio of intensities is 9:1, we can assign values to \( I_1 \) and \( I_2 \). Let’s assume:
\[ I_1 = 9 \quad \text{and} \quad I_2 = 1 \]

### Step 5: Find the possible combinations of intensities
The intensities can also be expressed in terms of two slits:
- One possible combination is \( I_1 = 5 \) and \( I_2 = 4 \).
- Another possible combination is \( I_1 = 4 \) and \( I_2 = 1 \).

### Step 6: Conclude the results
From the calculations, we can conclude:
- The intensity ratio \( I_1 : I_2 \) can be \( 4 : 1 \) or \( 5 : 4 \).
- The amplitude ratio \( A_1 : A_2 = 3 : 1 \).

### Final Answer
Thus, the intensity ratio between the bright and dark fringes implies that the intensities at the screen due to the two slits are either 5 and 4 units or 4 and 1 unit, and the amplitude ratio is 3:1.

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