If the intensity of light in double slit experiment from slit 1 and slit 2 are `l_(0)` and `25l_(0)` respectively, find the ratio of intensities of light at minima and maxima in the interference pattern.

Options

A. 0
B. `(4)/(9)`
C. `(24)/(26)`
D. `(4)/(6)`

Explanation

To solve the problem, we need to find the ratio of intensities at minima and maxima in the interference pattern created by two slits in a double slit experiment. Given that the intensity from slit 1 is \( I_0 \) and from slit 2 is \( 25I_0 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Intensities**:
- Let \( I_1 = I_0 \) (intensity from slit 1).
- Let \( I_2 = 25I_0 \) (intensity from slit 2).

2. **Calculate the Maximum Intensity**:
- The formula for the maximum intensity \( I_{\text{max}} \) in an interference pattern is given by:
\[ I_{\text{max}} = I_1 + I_2 + 2 \sqrt{I_1 I_2} \]
- Substituting the values:
\[ I_{\text{max}} = I_0 + 25I_0 + 2 \sqrt{I_0 \cdot 25I_0} \]
- Simplifying this:
\[ I_{\text{max}} = 26I_0 + 2 \sqrt{25I_0^2} = 26I_0 + 10I_0 = 36I_0 \]

3. **Calculate the Minimum Intensity**:
- The formula for the minimum intensity \( I_{\text{min}} \) in an interference pattern is given by:
\[ I_{\text{min}} = I_1 + I_2 - 2 \sqrt{I_1 I_2} \]
- Substituting the values:
\[ I_{\text{min}} = I_0 + 25I_0 - 2 \sqrt{I_0 \cdot 25I_0} \]
- Simplifying this:
\[ I_{\text{min}} = 26I_0 - 10I_0 = 16I_0 \]

4. **Find the Ratio of Intensities**:
- Now we can find the ratio of minimum intensity to maximum intensity:
\[ \text{Ratio} = \frac{I_{\text{min}}}{I_{\text{max}}} = \frac{16I_0}{36I_0} = \frac{16}{36} = \frac{4}{9} \]

### Final Answer:
The ratio of intensities at minima and maxima in the interference pattern is \( \frac{4}{9} \).