In YDSE, separation between slits is 0.15 mm, distance between slits and screen is 1.5 m and wavelength of light is 589 nm, then fringe width is

Options

A. 3.9mm
B. 4.7mm
C. 5.9mm
D. 3.7mm

Explanation

To find the fringe width in Young's Double Slit Experiment (YDSE), we can use the formula:

\[ \beta = \frac{\lambda D}{d} \]

where:
- \(\beta\) is the fringe width,
- \(\lambda\) is the wavelength of light,
- \(D\) is the distance from the slits to the screen, and
- \(d\) is the separation between the slits.

### Step 1: Convert the given values to SI units
- Wavelength \(\lambda = 589 \text{ nm} = 589 \times 10^{-9} \text{ m}\)
- Distance \(D = 1.5 \text{ m}\)
- Slit separation \(d = 0.15 \text{ mm} = 0.15 \times 10^{-3} \text{ m} = 1.5 \times 10^{-4} \text{ m}\)

### Step 2: Substitute the values into the formula
Now we can substitute the values into the formula for fringe width:

\[ \beta = \frac{(589 \times 10^{-9} \text{ m}) \times (1.5 \text{ m})}{(0.15 \times 10^{-3} \text{ m})} \]

### Step 3: Calculate the fringe width
Calculating the numerator:

\[ 589 \times 10^{-9} \times 1.5 = 883.5 \times 10^{-9} \text{ m} \]

Now calculating the denominator:

\[ 0.15 \times 10^{-3} = 1.5 \times 10^{-4} \text{ m} \]

Now substituting back into the formula:

\[ \beta = \frac{883.5 \times 10^{-9}}{1.5 \times 10^{-4}} \]

### Step 4: Simplify the expression
\[ \beta = \frac{883.5}{1.5} \times 10^{-5} = 589 \times 10^{-5} \text{ m} \]

### Step 5: Convert to millimeters
To convert from meters to millimeters:

\[ \beta = 589 \times 10^{-5} \text{ m} = 5.89 \text{ mm} \]

### Final Answer
Thus, the fringe width \(\beta\) is approximately:

\[ \beta \approx 5.89 \text{ mm} \]