Michelson Interferometer homework

[Ruth_1392]

Homework Statement

1. A Michelson interferometer is operated in a vacuum, using monochromatic
light of wavelength 589 nm. The interferometer is set up so that the distances
between the moving mirror and the beam splitter and the fixed mirror and the
beam splitter are equal. A parallel-sided object 1.2 cm in length and refractive
index 1.4900 is then placed between the fixed mirror and the beam splitter.
i. Calculate the optical path length of the interposed material.
ii. What is the wavelength of the light in the interposed material?
iii. What is the change in the optical path length of the fixed arm that results?
iv. What would be the required dimension of a parallel-sided object of refractive
index 1.6618 placed between the moving mirror and the beam splitter to
ensure that both arms had the same optical path length?

Homework Equations

optical path length= distance traveled in medium x refractive index

λ₁ = λ₀ / refractive index

The Attempt at a Solution

I have done parts i) and ii) I got 0.01788m for i) and 395nm for ii). I'm not sure about parts iii) and iv), I think that part iii) uses the answer for part ii) but I don't know how. I found in my notes that Optical path difference = 2L₁ - 2L₂ but I'm not sure if it's useful and also I don't know the values for L. With part iv) I think I would use optical path length= distance traveled in medium x refractive index using the value for iii) and the refractive index given.

 

[AvroArrow]

I'm not sure if this is correct or how to do the calculation.Any help would be greatly appreciated. Thanks!