In double slit experiment , the distance between two slits is `0.6mm` and these are illuminated with light of wavelength `4800 Å`. The angular width of dark fringe on the screen at a distance 120 cm from slits will be

Options

A. `8xx10^(-4)` radian
B. `6xx10^(-4)` radian
C. `4xx10^(-4)` radian
D. `16xx10^(-4)` radian

Explanation

To solve the problem of finding the angular width of the dark fringe in a double slit experiment, we can follow these steps:

### Step 1: Understand the given values
- Distance between the two slits (d) = 0.6 mm = 0.6 × 10^-3 m
- Wavelength of light (λ) = 4800 Å = 4800 × 10^-10 m = 4.8 × 10^-7 m
- Distance from the slits to the screen (D) = 120 cm = 1.2 m

### Step 2: Use the formula for angular width of dark fringe
The angular width (θ) of the dark fringe in a double slit experiment can be given by the formula:
\[ \theta = \frac{\lambda}{d} \]
where:
- λ is the wavelength of the light used,
- d is the distance between the two slits.

### Step 3: Substitute the values into the formula
Now, substituting the known values into the formula:
\[ \theta = \frac{4.8 \times 10^{-7} \text{ m}}{0.6 \times 10^{-3} \text{ m}} \]

### Step 4: Calculate θ
Calculating the above expression:
\[ \theta = \frac{4.8 \times 10^{-7}}{0.6 \times 10^{-3}} = \frac{4.8}{0.6} \times 10^{-4} = 8 \times 10^{-4} \text{ radians} \]

### Step 5: Convert radians to degrees (if necessary)
To convert radians to degrees, we can use the conversion factor \( \frac{180}{\pi} \):
\[ \theta \text{ (in degrees)} = 8 \times 10^{-4} \times \frac{180}{\pi} \approx 0.046 \text{ degrees} \]

### Final Answer
The angular width of the dark fringe is approximately \( 8 \times 10^{-4} \) radians or \( 0.046 \) degrees.

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