In`YDSE`,how many maxima can be obtained on the screen if wavelength of light used is `200nm`and `d=700nm`:

Options

A. `12`
B. `7`
C. `18`
D. none of these

Explanation

To solve the problem of how many maxima can be obtained on the screen in Young's Double Slit Experiment (YDSE) with a wavelength of light \( \lambda = 200 \, \text{nm} \) and slit separation \( d = 700 \, \text{nm} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Condition for Maxima**:
In YDSE, maxima occur due to constructive interference. The condition for constructive interference is given by:
\[ d \sin \theta = n \lambda \]
where \( n \) is an integer (0, 1, 2, ...), \( d \) is the distance between the slits, and \( \lambda \) is the wavelength of light.

2. **Finding the Maximum Value of \( n \)**:
To find the maximum number of maxima, we need to determine the largest integer \( n \) such that:
\[ n \lambda \leq d \]
Rearranging this gives:
\[ n \leq \frac{d}{\lambda} \]

3. **Substituting the Given Values**:
Now we substitute the values of \( d \) and \( \lambda \):
\[ n \leq \frac{700 \, \text{nm}}{200 \, \text{nm}} = 3.5 \]

4. **Determining the Maximum Integer \( n \)**:
Since \( n \) must be an integer, the maximum value of \( n \) is:
\[ n_{\text{max}} = 3 \]

5. **Calculating the Total Number of Maxima**:
The total number of maxima observed on the screen is given by the formula:
\[ \text{Total Maxima} = 2n + 1 \]
Substituting \( n_{\text{max}} = 3 \):
\[ \text{Total Maxima} = 2 \times 3 + 1 = 7 \]

### Final Answer:
Thus, the total number of maxima that can be obtained on the screen is **7**.

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