Physical optics -- counting interfence fringes to measure a length change

[denniszhao]

Homework Statement

Monochromatic light with wavelength λ=650nm is used to determine the coefficient of thermal expansion, α, of a particular metal. The apparatus is shown below. Light is projected from above and passes through the glass and reflects off the cylinder with initial length l0=15.0cm. The gap between the glass and the cylinder is very thin. Consequently, the reflected light contains an interference pattern with alternating light and dark fringes. As the temperature of the cylinder is raised, it expands and the width of the gap decreases. A researcher observes 450 fringe shifts when the temperature increases by ∆T=40.0K. What is the coefficient of thermal expansion for the metal?
I was tryna combine this two formulas to find out the thermal expansion coefficient α but the answer is incorrect.

Relevant Equations

Thermal expansion: ∆l=l0*α*∆T
Optics: ∆l=mλ

 

[BvU]

I was tryna combine this two formulas to find out the thermal expansion coefficient α but the answer is incorrect.

Post your work, so we can try to find why and from where ...

Guidelines

 

[kuruman]

It looks like you did not consider that the light travels twice the distance between the back of the glass and the end of the rod.