Question

In Young's Double Slit Experiment, if the wavelength of light used is doubled while keeping all other quantities constant, the fringe width becomes:

• A. Half
• B. Double
• C. Four times
• D. Unchanged

Hint:

In YDSE: \[ \beta=\frac{\lambda D}{d} \] Fringe width increases with: \[ \text{increase in wavelength} \]

Answer 1

The Correct Option is B

In Young's Double Slit Experiment, fringe width is given by: \[ \beta=\frac{\lambda D}{d} \] where:
• \(\beta\) = fringe width
• \(\lambda\) = wavelength of light
• \(D\) = distance between screen and slits
• \(d\) = distance between slits
Step 1: Observe the relation
From the formula: \[ \beta \propto \lambda \] Thus fringe width is directly proportional to wavelength.

Step 2: Double the wavelength
If: \[ \lambda \rightarrow 2\lambda \] then: \[ \beta \rightarrow 2\beta \] Hence fringe width becomes: \[ \text{double} \] Option analysis:
• Option (A): Incorrect
• Option (B): Correct
• Option (C): Incorrect
• Option (D): Incorrect Therefore: \[ \boxed{\text{(B)}} \]