In YDSE, the distance between the slits is 1 m m and screen is 25cm away from the slits . If the wavelength of light is `6000 Å` , the fringe width on the secreen is

Options

A. 0 . 15 m m
B. 0 . 30 m m
C. 0 . 24 m m
D. 0 . 12 m m

Answer

To solve the problem, we need to find the fringe width in Young's Double Slit Experiment (YDSE) using the given parameters. Let's break it down step by step.

### Step 1: Identify the given values
- Distance between the slits (d) = 1 mm = \(1 \times 10^{-3}\) m
- Distance from the slits to the screen (D) = 25 cm = \(25 \times 10^{-2}\) m
- Wavelength of light (λ) = 6000 Å = \(6000 \times 10^{-10}\) m

### Step 2: Write the formula for fringe width
The formula for fringe width (β) in YDSE is given by:
\[ \beta = \frac{\lambda D}{d} \]

### Step 3: Substitute the values into the formula
Now, we will substitute the values we have into the formula:
\[ \beta = \frac{6000 \times 10^{-10} \text{ m} \times 25 \times 10^{-2} \text{ m}}{1 \times 10^{-3} \text{ m}} \]

### Step 4: Perform the calculation
Calculating the numerator:
\[ 6000 \times 10^{-10} \times 25 \times 10^{-2} = 150000 \times 10^{-12} = 1.5 \times 10^{-7} \text{ m} \]

Now, divide by \(1 \times 10^{-3}\):
\[ \beta = \frac{1.5 \times 10^{-7}}{1 \times 10^{-3}} = 1.5 \times 10^{-4} \text{ m} \]

### Step 5: Convert to mm
To convert meters to millimeters, we multiply by \(1000\):
\[ \beta = 1.5 \times 10^{-4} \text{ m} \times 1000 = 0.15 \text{ mm} \]

### Final Answer
The fringe width on the screen is \(0.15 \text{ mm}\).

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