A thin film with an index of refraction of 1.60 is placed in one of the beams of a Michelson interferometer.If this causes a shift of 8 bright fringes in the pattern produced by light of wavelength 580 nm, what is the thickness of the film?
A)1.5 µm
B)2.9 µm
C)3.9 µm
D)7.7 µm
E)16 µm

Question

Quizplus · Accepted Answer

The shift in the fringe pattern is given by:
$\Delta m = \frac{2t}{\lambda}(n-1)$ where $t$ is the thickness of the film, $\lambda$ is the wavelength of light, $n$ is the refractive index of the film and $\Delta m$ is the number of fringes shifted.

Rearranging the equation, we get:
$t = \frac{\Delta m \lambda}{2(n-1)}$

Substituting the given values, we get:
$t = \frac{8\cdot 580	imes 10^{-9}}{2(1.6-1)} = 3.9\ \mu m$

Therefore, the thickness of the film is 3.9 µm, which is option C.

A Thin Film with an Index of Refraction of 1