# Angular radius in michelson interferometer

• kelambumlm
So in summary, to find the angular radius of the tenth bright fringe in a Michelson interferometer, you need to use the equation 2d sin theta = m lambda, where d is the distance between the two mirrors, theta is the angular radius of the fringe, m is the order of the fringe, and lambda is the wavelength of the light used. By substituting the given values into this equation, we can find the angular radius of the tenth bright fringe for two different central-path differences (1.50 mm and 1.5 cm), which both
kelambumlm

## Homework Statement

Find the angular radius of the tenth bright fringe in a Michelson interferometer
when the central-path difference (2d) is (i) 1.50 mm and (ii) 1.5 cm.
Assume the orange light of a krypton arc is used and that the interference is
adjusted in each case so that the first bright fringe forms a maximum at the
centre of the pattern.

## Homework Equations

2d sin theta = m lambda or
2d cos theta= m lamda

## The Attempt at a Solution

i confuse to use the equation.

theta= cos or sin -1 (6057 armstrong x 10th) divide 1.50mm
the answer that i get is not logic.

Hello,

To solve this problem, you will need to use the equation 2d sin theta = m lambda, where d is the distance between the two mirrors in the Michelson interferometer, theta is the angular radius of the fringe, m is the order of the fringe, and lambda is the wavelength of the light used.

In this case, we are given that the central-path difference (2d) is 1.50 mm and that we are using orange light from a krypton arc, which has a wavelength of 6057 Armstrongs. We are also told that the first bright fringe forms a maximum at the centre of the pattern, which means that m = 1.

Substituting these values into the equation, we get:

2(1.50 mm) sin theta = (1)(6057 Armstrongs)

Solving for theta, we get:

theta = sin -1 (6057 Armstrongs / 3.00 mm) = 0.383 radians

To find the angular radius of the tenth bright fringe, we need to multiply this value by 10, since the order of the fringe is now m = 10. So the angular radius of the tenth bright fringe would be:

To convert this to degrees, we can use the conversion factor of 180 degrees / pi radians, so the angular radius of the tenth bright fringe would be:

So the angular radius of the tenth bright fringe in this case would be 219.6 degrees.

For the second part of the problem, where the central-path difference is 1.5 cm, we can use the same equation, but with different values:

2(1.5 cm) sin theta = (1)(6057 Armstrongs)

Solving for theta, we get:

theta = sin -1 (6057 Armstrongs / 3.00 cm) = 0.383 radians

Again, to find the angular radius of the tenth bright fringe, we multiply this value by 10, since the order of the fringe is now m = 10. So the angular radius of the tenth bright fringe would be:

To convert this to degrees, we can use the conversion factor of 180 degrees /

## 1. What is the purpose of using a Michelson interferometer to measure angular radius?

The Michelson interferometer is a precise instrument used to measure small angles, such as the angular radius of an object. This measurement is important in various fields of science, including astronomy, where it is used to determine the size and distance of celestial objects.

## 2. How does a Michelson interferometer work to measure angular radius?

The Michelson interferometer works by splitting a beam of light into two parts and then recombining them to create an interference pattern. The angular radius is measured by observing the shifting of this interference pattern caused by the angle of the object being measured.

## 3. What are the advantages of using a Michelson interferometer over other methods of measuring angular radius?

Compared to other methods, the Michelson interferometer offers a higher level of precision and accuracy. It is also relatively simple and can be used to measure both small and large angular radii.

## 4. Can a Michelson interferometer be used to measure the angular radius of any object?

In theory, a Michelson interferometer can be used to measure the angular radius of any object as long as it is within the range of the instrument's capabilities. However, the object must have a reflective surface for the instrument to work effectively.

## 5. Are there any limitations to using a Michelson interferometer to measure angular radius?

One limitation of using a Michelson interferometer is that it requires a stable and controlled environment to obtain accurate measurements. Any external factors, such as vibrations or air currents, can affect the interference pattern and result in inaccurate readings.

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