In a Young’s double slit experiment, 16 fringes are observed in a certain segment of the screen when light of wavelength 700 nm is used. If the wavelength of light is changed to 400 nm, the number of fringes observed in the same segment of the screen would be:

Options

A. 28
B. 24
C. 30
D. 18

Explanation

To solve the problem, we need to determine how many fringes will be observed on the screen when the wavelength of light is changed from 700 nm to 400 nm, given that 16 fringes are observed with the 700 nm wavelength.

### Step-by-Step Solution:

1. **Understanding the Fringe Width**:
The fringe width (β) in a Young's double slit experiment is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \lambda \) = wavelength of light
- \( D \) = distance from the slits to the screen
- \( d \) = distance between the slits

2. **Number of Fringes**:
The number of fringes (N) observed in a certain segment of the screen can be expressed as:
\[ N = \frac{L}{\beta} \]
where \( L \) is the length of the segment of the screen being considered.

3. **Setting Up the Equation**:
For the first case with \( \lambda_1 = 700 \, \text{nm} \):
\[ N_1 = \frac{L}{\beta_1} = \frac{L}{\frac{\lambda_1 D}{d}} = \frac{L \cdot d}{\lambda_1 D} \]
Given \( N_1 = 16 \), we have:
\[ 16 = \frac{L \cdot d}{700 \times 10^{-9} \cdot D} \]

4. **For the Second Wavelength**:
For the second case with \( \lambda_2 = 400 \, \text{nm} \):
\[ N_2 = \frac{L}{\beta_2} = \frac{L}{\frac{\lambda_2 D}{d}} = \frac{L \cdot d}{\lambda_2 D} \]
We need to find \( N_2 \):
\[ N_2 = \frac{L \cdot d}{400 \times 10^{-9} \cdot D} \]

5. **Relating the Two Cases**:
Since \( L \), \( d \), and \( D \) remain constant, we can set up the ratio:
\[ \frac{N_1}{N_2} = \frac{\lambda_2}{\lambda_1} \]
Plugging in the values:
\[ \frac{16}{N_2} = \frac{400}{700} \]

6. **Solving for \( N_2 \)**:
Rearranging gives:
\[ N_2 = 16 \cdot \frac{700}{400} \]
Simplifying:
\[ N_2 = 16 \cdot \frac{7}{4} = 16 \cdot 1.75 = 28 \]

### Final Answer:
The number of fringes observed when the wavelength is changed to 400 nm is **28**.