In double slit experiment using light of wavelength `600 nm`, the angular width of a fringe formed on a distant screen is `0.1^(@)`. What is the spacing between the two slits ?

Options

A. `3.44xx10^(-4)m`
B. `1.54xx10^(-4)m`
C. `1.54xx10^(-3)m`
D. `1.44xx10^(-3)m`

Explanation

To find the spacing between the two slits in a double slit experiment, we can use the relationship between the wavelength of light, the angular width of the fringe, and the slit spacing. The formula we will use is:

\[ d = \frac{\lambda}{\theta} \]

Where:
- \( d \) is the spacing between the slits,
- \( \lambda \) is the wavelength of the light,
- \( \theta \) is the angular width of the fringe in radians.

### Step-by-Step Solution:

1. **Identify the given values:**
- Wavelength \( \lambda = 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m} \)
- Angular width \( \theta = 0.1^\circ \)

2. **Convert the angular width from degrees to radians:**
- Use the conversion factor \( \frac{\pi}{180} \) to convert degrees to radians.
\[ \theta = 0.1 \times \frac{\pi}{180} = \frac{0.1 \pi}{180} \, \text{radians} \]

3. **Substitute the values into the formula:**
- Now, substitute \( \lambda \) and \( \theta \) into the formula for \( d \):
\[ d = \frac{600 \times 10^{-9}}{\frac{0.1 \pi}{180}} \]

4. **Calculate the denominator:**
- First, calculate \( \frac{0.1 \pi}{180} \):
\[ \frac{0.1 \pi}{180} \approx 0.00174533 \, \text{radians} \]

5. **Calculate the spacing \( d \):**
- Now substitute this value back into the equation for \( d \):
\[ d = \frac{600 \times 10^{-9}}{0.00174533} \approx 3.44 \times 10^{-4} \, \text{m} \]

6. **Convert to a more convenient unit if necessary:**
- The spacing can also be expressed in micrometers:
\[ d \approx 344 \, \mu m \]

### Final Answer:
The spacing between the two slits is approximately \( 3.44 \times 10^{-4} \, \text{m} \) or \( 344 \, \mu m \).