In YDSE wavelength of light used is 500 nm and slit width is `0.05 mm`. then the angular fringe width will be.

Options

A. `1.8^@`
B. `3.2^@`
C. `0.57^@`
D. `0.48^@`

Answer

To find the angular fringe width in the Young's Double Slit Experiment (YDSE), we can follow these steps:

### Step 1: Understand the formula for fringe width
The fringe width (β) in YDSE is given by the formula:
\[ \beta = \frac{\lambda D}{d} \]
where:
- \( \lambda \) = wavelength of light
- \( D \) = distance from the slits to the screen
- \( d \) = distance between the slits

For angular fringe width, we can relate it to the fringe width using:
\[ \text{Angular Fringe Width} = \frac{\beta}{D} \]
Thus, we can express the angular fringe width as:
\[ \text{Angular Fringe Width} = \frac{\lambda}{d} \]

### Step 2: Convert the given values into standard units
Given:
- Wavelength (\( \lambda \)) = 500 nm = \( 500 \times 10^{-9} \) m
- Slit width (\( d \)) = 0.05 mm = \( 0.05 \times 10^{-3} \) m = \( 5 \times 10^{-5} \) m

### Step 3: Substitute the values into the formula
Now, we can substitute the values into the formula for angular fringe width:
\[ \text{Angular Fringe Width} = \frac{\lambda}{d} = \frac{500 \times 10^{-9}}{5 \times 10^{-5}} \]

### Step 4: Simplify the expression
Calculating the above expression:
\[ \text{Angular Fringe Width} = \frac{500 \times 10^{-9}}{5 \times 10^{-5}} = \frac{500}{5} \times \frac{10^{-9}}{10^{-5}} = 100 \times 10^{-4} = 1 \times 10^{-2} \text{ radians} \]

### Step 5: Convert radians to degrees
To convert radians to degrees, we use the conversion factor:
\[ 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} \]
Thus,
\[ \text{Angular Fringe Width in degrees} = 1 \times 10^{-2} \times \frac{180}{\pi} \approx 0.57 \text{ degrees} \]

### Final Answer
The angular fringe width is approximately \( 0.57 \) degrees.

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