In Young's double slit experiment, the distance between the two slits is 0.1 mm, the distance between the screen and the slit is 100 cm. if the width of the fringe is 5 mm, then the wavelength of monochromatic light used is

Options

A. 4000 Å
B. 6000 Å
C. 5000 Å
D. 5400 Å

Explanation

To solve the problem step by step, we will use the formula for the fringe width in Young's double slit experiment.

### Step 1: Understand the given values
- Distance between the two slits (d) = 0.1 mm = \(0.1 \times 10^{-3}\) m = \(1 \times 10^{-4}\) m
- Distance from the slits to the screen (D) = 100 cm = \(100 \times 10^{-2}\) m = 1 m
- Width of the fringe (X) = 5 mm = \(5 \times 10^{-3}\) m

### Step 2: Write the formula for fringe width
The formula for the fringe width (X) in Young's double slit experiment is given by:
\[ X = \frac{D \lambda}{d} \]
where:
- \(X\) is the fringe width,
- \(D\) is the distance from the slits to the screen,
- \(d\) is the distance between the slits,
- \(\lambda\) is the wavelength of the light used.

### Step 3: Rearrange the formula to find the wavelength (\(\lambda\))
To find the wavelength, we rearrange the formula:
\[ \lambda = \frac{X d}{D} \]

### Step 4: Substitute the values into the formula
Now, substituting the values we have:
\[ \lambda = \frac{(5 \times 10^{-3} \, \text{m}) \times (1 \times 10^{-4} \, \text{m})}{1 \, \text{m}} \]

### Step 5: Calculate the wavelength
Calculating the above expression:
\[ \lambda = \frac{5 \times 10^{-3} \times 1 \times 10^{-4}}{1} = 5 \times 10^{-7} \, \text{m} \]

### Step 6: Convert the wavelength to Angstroms
1 Angstrom = \(10^{-10}\) m, so:
\[ \lambda = \frac{5 \times 10^{-7}}{10^{-10}} = 5 \times 10^{3} \, \text{Angstroms} \]

### Step 7: Final result
Thus, the wavelength of the monochromatic light used is:
\[ \lambda = 5000 \, \text{Angstroms} \]

### Summary of the solution
The wavelength of the monochromatic light used in Young's double slit experiment is \(5000 \, \text{Angstroms}\).

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