What is the wavelength of the light in the interposed material?

[RWalker1987]

Homework Statement

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.

What is the change in the optical path length of the fixed arm that results?

Homework Equations

this is were I'm stuck, I don't know what equation to use, I have looked all over for an equation, but most use frequency

The Attempt at a Solution

 

[gabbagabbahey]

What is the relationship between wavelength and frequency? ;0)