Angular radius in michelson interferometer

[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.

 

[Jhero]

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:

theta = (10)(0.383 radians) = 3.83 radians

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:

theta = (3.83 radians)(180 degrees / pi radians) = 219.6 degrees

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:

theta = (10)(0.383 radians) = 3.83 radians

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