Question

One of the beams of an interferometer (Fig. 24-59) passes through a small glass container containing a cavity 1.30 cm deep. When a gas is allowed to slowly fill the container, a total of 224 dark fringes are counted to move past a reference line. The light used has a wavelength of 530 nm. Calculate the index of refraction of the gas, assuming that the interferometer is in vacuum. (Give your answer to 4 decimal places.)

Answer 1

number of fringes shifted when the glass container is filled with the gas is \(\Delta m=(n-1) \frac{2 d}{\lambda}\)

Here \(n\) is the refractive index of the gas, \(d\) is the

length of the container, and \(\lambda\) is the wavelength of the

light used.

Rearrange equation for \(n .\) \(n=1+\frac{\lambda \Delta m}{2 d}\)

Substitute \(530 \times 10^{-9} \mathrm{~m}\) for \(\lambda, 224\) for \(\Delta m, 1.3 \times 10^{-2} \mathrm{~m}\)

for \(d\) and solve for \(n\).

\(n=1+\frac{\left(530 \times 10^{-9} \mathrm{~m}\right)(224)}{2\left(1.3 \times 10^{-2} \mathrm{~m}\right)}\)

\(=1.005\)