Question

In a Michelson interferometer, one fringe shift corresponds to a mirror displacement of

• A. \(\lambda\)
• B. \(\dfrac{\lambda}{2}\)
• C. \(\dfrac{\lambda}{4}\)
• D. \(2\lambda\)

Hint:

For a Michelson interferometer, \[ \boxed{ 2d=m\lambda } \] For one fringe shift (\(m=1\)), \[ \boxed{ d=\frac{\lambda}{2}. } \]

Answer 1

The Correct Option is B

Step 1: Recall the optical path difference. In a Michelson interferometer, if the mirror is displaced by a distance \(d\), the optical path difference changes by \[ 2d. \]

Step 2: Apply the condition for one fringe shift. One fringe shift occurs when the optical path difference changes by one wavelength: \[ 2d=\lambda. \] Therefore, \[ d=\frac{\lambda}{2}. \] Hence, \[ \boxed{\frac{\lambda}{2}} \] is the required mirror displacement. Therefore, \[ \boxed{(B)} \] is the correct answer.