With two slits spaced 0.2 mm apart and a screen at a distance of 1 m, the third bright fringe is found to be at 7.5 mm from the central fringe. The wavelength of light used is

Options

A. 400nm
B. 500nm
C. 550nm
D. 600nm

Explanation

To find the wavelength of light used in the double-slit experiment, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Distance between the slits (d) = 0.2 mm = \(0.2 \times 10^{-3}\) m
- Distance from the slits to the screen (D) = 1 m
- Distance of the third bright fringe from the central fringe (y) = 7.5 mm = \(7.5 \times 10^{-3}\) m
- Order of the fringe (n) = 3 (since we are looking for the third bright fringe)

2. **Use the formula for the position of the nth bright fringe**:
\[ y_n = \frac{n \lambda D}{d} \]
where \(y_n\) is the distance from the central maximum to the nth bright fringe.

3. **Substitute the known values into the formula**:
For the third bright fringe (n = 3):
\[ y_3 = \frac{3 \lambda D}{d} \]
Rearranging the formula to solve for \(\lambda\):
\[ \lambda = \frac{y_3 \cdot d}{3D} \]

4. **Substitute the values**:
\[ \lambda = \frac{(7.5 \times 10^{-3} \text{ m}) \cdot (0.2 \times 10^{-3} \text{ m})}{3 \cdot (1 \text{ m})} \]

5. **Calculate \(\lambda\)**:
\[ \lambda = \frac{(7.5 \times 10^{-3}) \cdot (0.2 \times 10^{-3})}{3} \]
\[ \lambda = \frac{1.5 \times 10^{-6}}{3} = 0.5 \times 10^{-6} \text{ m} = 500 \text{ nm} \]

### Final Answer:
The wavelength of light used is \(500 \text{ nm}\).