In Young's double slit experiment, the angular width of a fringe formed on a distant screen is `0.1^(@)`. What is the spacing between the slits, if the waveelngth of light used is 6000 Å?

Options

A. `3.44xx10^(-4)m`
B. `2.44xx10^(-4)m`
C. `1.44xx10^(-4)m`
D. `5.44xx10^(-4)`m

Explanation

To solve the problem of finding the spacing between the slits in Young's double slit experiment, we can follow these steps:

### Step 1: Understand the Given Data
We are given:
- Angular width of the fringe (θ) = 0.1 degrees
- Wavelength of light (λ) = 6000 Å = 6000 x 10^(-10) meters

### Step 2: Convert Angular Width to Radians
To use the angular width in calculations, we need to convert degrees to radians. The conversion formula is:
\[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \]
Thus,
\[ \theta = 0.1 \times \frac{\pi}{180} \]

### Step 3: Calculate the Value of θ in Radians
Using the value of π (approximately 3.142):
\[ \theta = 0.1 \times \frac{3.142}{180} \approx 0.00174533 \text{ radians} \]

### Step 4: Use the Formula for Angular Width
In Young's double slit experiment, the angular width (θ) of the fringe is given by the formula:
\[ \theta = \frac{\lambda}{d} \]
where:
- λ is the wavelength of light
- d is the spacing between the slits

### Step 5: Rearrange the Formula to Solve for d
Rearranging the formula to find the spacing (d):
\[ d = \frac{\lambda}{\theta} \]

### Step 6: Substitute the Values
Now we can substitute the values of λ and θ into the equation:
\[ d = \frac{6000 \times 10^{-10}}{0.00174533} \]

### Step 7: Calculate d
Calculating the above expression:
\[ d \approx \frac{6000 \times 10^{-10}}{0.00174533} \approx 3.44 \times 10^{-4} \text{ meters} \]

### Step 8: Final Answer
Thus, the spacing between the slits is:
\[ d \approx 3.44 \times 10^{-4} \text{ meters} \]

### Summary
The spacing between the slits in Young's double slit experiment is approximately **3.44 x 10^(-4) meters**.

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