Answer to Question #99326 in Optics for Ra

Question

A transparent filen of glass of refractive index 1.5 is introduced normally in the path of one of the interfering beams of a Michelson interferometer which is illuminated with a light of wavelength 4800 angstrom. This causes 500 dark fringes to sweep across the field. To determine the thickness of the film.

Answer 1

We can writer for Michelson Interferometer

without the film

$Δ_1=2dn_0-2tn_0=m_1 λ (1)$

with the film

$Δ_2=2ln+2(d-l)n_0-2tn_0=m_2 λ (2)$

where d, t is the Michelson Interferometer arms lengths.

Using (1) and (2) we got

$Δ= Δ_1- Δ_2=2ln-2ln_0=(m_2-m_1)λ (3)$

In our case, n=1.5, n₀=1, m₂-m₁=500, λ=4800 angstrom

l=120×10^-6 m

Answer

120×10^-6 m