Two slits in Young's double slit experiment have widths in the ratio 81:1. What is the the ratio of amplitudes of light waves coming from them ?

Options

A. `3:1`
B. `3:2`
C. `9:1`
D. `6:1`

Explanation

To solve the problem of finding the ratio of amplitudes of light waves coming from two slits in Young's double slit experiment, given that their widths are in the ratio of 81:1, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between slit width and intensity**:
The intensity of light passing through a slit is directly proportional to the square of the amplitude of the wave and the width of the slit. Therefore, if the widths of the slits are W1 and W2, we can express the relationship as:
\[ \frac{I_1}{I_2} = \frac{W_1}{W_2} \]

2. **Assign the widths**:
Given that the widths are in the ratio 81:1, we can assign:
\[ W_1 = 81k \quad \text{and} \quad W_2 = 1k \]
for some constant \( k \).

3. **Express the intensity ratio**:
Using the widths, we can write:
\[ \frac{I_1}{I_2} = \frac{W_1}{W_2} = \frac{81k}{1k} = 81 \]

4. **Relate intensity to amplitude**:
Since intensity is proportional to the square of the amplitude, we have:
\[ \frac{I_1}{I_2} = \frac{A_1^2}{A_2^2} \]

5. **Set up the equation**:
From the intensity ratio we derived:
\[ \frac{A_1^2}{A_2^2} = 81 \]

6. **Take the square root**:
To find the ratio of amplitudes, we take the square root of both sides:
\[ \frac{A_1}{A_2} = \sqrt{81} = 9 \]

7. **Write the final ratio**:
Therefore, the ratio of the amplitudes of the light waves coming from the two slits is:
\[ A_1 : A_2 = 9 : 1 \]

### Final Answer:
The ratio of amplitudes of light waves coming from the two slits is \( 9 : 1 \).

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