# Michelson interferometer moves and bright fringes disappear

• Cocoleia
In summary, the conversation discusses using a Michelson interferometer to determine the distance a mirror has been moved based on the disappearance of 250 bright fringes into the center. The formula 2d=mλ is mentioned as a way to calculate this distance, but there is uncertainty about how to derive it. The question also raises the point of how the corresponding optical path length changes when a mirror is translated over a certain amount, such as λ/2 or 2λ/2.
Cocoleia

## Homework Statement

In a Michelson interferometer, as one of the mirrors is moved, 250 bright fringes disappear into the centre. If the light wavelength was 800nm, how far was the mirror moved?

## The Attempt at a Solution

My logic is:
If we were to count how many passing bright fringes we have, we could find the wavelength, basing ourselves off of the formula: 2d=mλ. In this case I would say 2Δd=Δmλ, where Δd is the distance that the mirror moved and Δm is the number of passing bright fringes.
So I would solve for Δd and get 0.01cm
My problem is, I am pretty sure I need to somehow derive 2d=mλ, I can't just use it. Can someone get me started on how to derive this?
Also, is my logic correct

What happens to the corresponding optical path length if a mirror is translated over ##\lambda\over 2 ## ? Idem ## {2\lambda\over 2}, {3\lambda\over 2} ##, etc ?

## 1. How does a Michelson interferometer work?

A Michelson interferometer uses a beam splitter to split a single beam of light into two separate beams. One beam travels to a fixed mirror, while the other travels to a movable mirror. The two beams are then recombined and the resulting interference pattern is observed.

## 2. Why do the bright fringes disappear when the movable mirror is moved?

The bright fringes in a Michelson interferometer are created by constructive interference, where the peaks of the two beams align. When the movable mirror is moved, the path length of one of the beams changes, causing the interference pattern to shift and the fringes to disappear.

## 3. How does the movement of the movable mirror affect the interference pattern?

The movement of the movable mirror changes the path length of one of the beams, which results in a change in the phase difference between the two beams. This change in phase difference causes the interference pattern to shift or disappear.

## 4. What is the purpose of using a Michelson interferometer?

A Michelson interferometer is commonly used in scientific experiments to measure small changes in distance, wavelength, or refractive index. It can also be used to study the properties of light, such as interference and polarization.

## 5. Can a Michelson interferometer be used to measure the speed of light?

Yes, a Michelson interferometer can be used to measure the speed of light. By measuring the path length difference between the two beams and the time it takes for the interference pattern to change, the speed of light can be calculated using the equation c = 2d / t, where c is the speed of light, d is the path length difference, and t is the time difference.

Replies
0
Views
571
• Introductory Physics Homework Help
Replies
8
Views
4K
• Introductory Physics Homework Help
Replies
6
Views
3K
• Introductory Physics Homework Help
Replies
1
Views
2K
• Optics
Replies
2
Views
880
• Introductory Physics Homework Help
Replies
1
Views
1K
• Special and General Relativity
Replies
9
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
3K
• Introductory Physics Homework Help
Replies
2
Views
1K
• Other Physics Topics
Replies
7
Views
3K