Young's experiment is performed with light of wavelength 6000 Å wherein 16 fringes occupy a certain region on the screen. If 24 fringes occupy the same region with another light of wavelength `lambda`, then `lambda` is

Options

A. 6000 Å
B. 4500 Å
C. 5000 Å
D. 4000 Å

Explanation

To solve the problem, we will use the relationship between the number of fringes, the wavelength of light, and the distance between the slits and the screen in Young's double-slit experiment.

### Step-by-Step Solution:

1. **Understand the relationship**: In Young's experiment, the position of the fringes on the screen is given by the formula:
\[ y = \frac{n \lambda D}{d} \]
where \( y \) is the fringe position, \( n \) is the number of fringes, \( \lambda \) is the wavelength of light, \( D \) is the distance from the slits to the screen, and \( d \) is the distance between the slits.

2. **Set up the equation for the first wavelength**: For the first light of wavelength \( \lambda_1 = 6000 \, \text{Å} \) (or \( 6000 \times 10^{-10} \, \text{m} \)), and with \( n_1 = 16 \) fringes occupying a certain region, we can express the position as:
\[ y_1 = n_1 \lambda_1 = 16 \times 6000 \, \text{Å} \]

3. **Set up the equation for the second wavelength**: For the second light of wavelength \( \lambda_2 \) with \( n_2 = 24 \) fringes occupying the same region, we can express the position as:
\[ y_2 = n_2 \lambda_2 = 24 \lambda_2 \]

4. **Equate the positions**: Since both \( y_1 \) and \( y_2 \) represent the same physical distance on the screen, we can set them equal to each other:
\[ 16 \times 6000 \, \text{Å} = 24 \lambda_2 \]

5. **Solve for \( \lambda_2 \)**: Rearranging the equation gives:
\[ \lambda_2 = \frac{16 \times 6000 \, \text{Å}}{24} \]

6. **Calculate \( \lambda_2 \)**:
\[ \lambda_2 = \frac{96000 \, \text{Å}}{24} = 4000 \, \text{Å} \]

### Final Answer:
Thus, the wavelength \( \lambda \) is:
\[ \lambda = 4000 \, \text{Å} \]