Question

Two slits 4 mm apart, are illuminated by light of wavelength 6000 A. What will be the fringe width on a screen placed 2 m from the slits?

• A. 0.12 mm
• B. 0.3 mm
• C. 3.0 mm
• D. 4.0 mm

Hint:

To find the fringe width in an interference pattern, use the formula \( \beta = \frac{\lambda D}{d} \), where \( \lambda \) is the wavelength, \( D \) is the distance to the screen, and \( d \) is the slit separation.

Answer 1

The Correct Option is B

Step 1: Understanding the interference pattern.
In an interference experiment, the fringe width (\( \beta \)) is given by the formula: \[ \beta = \frac{\lambda D}{d} \] where: - \( \lambda \) is the wavelength of light, - \( D \) is the distance between the slits and the screen, - \( d \) is the distance between the two slits.

Step 2: Substituting known values.
From the question: - \( \lambda = 6000 \, \text{Å} = 6000 \times 10^{-10} \, \text{m} \), - \( D = 2 \, \text{m} \), - \( d = 4 \, \text{mm} = 4 \times 10^{-3} \, \text{m} \).
Using the formula for fringe width: \[ \beta = \frac{(6000 \times 10^{-10}) (2)}{4 \times 10^{-3}} = 0.3 \, \text{mm} \]

Step 3: Conclusion.
The fringe width is \( 0.3 \, \text{mm} \). Therefore, the correct answer is (2).