Question

A Michelson interferometer operating at a $600nm$wavelength has a $2.00-cm$-long glass cell in one arm. To begin, the air is pumped out of the cell and mirror $M2$is adjusted to produce a bright spot at the center of the interference pattern. Then a valve is opened and air is slowly admitted into the cell. The index of refraction of air at $1.00atm$pressure is $1.00028$. How many brightdark-bright fringe shifts are observed as the cell fills with air?

Short answer

$19$brightdark-bright fringe shifts are observed as the cell fills with air.

Step-by-step solution

Introduction

The wavelength of a waveform signal carried in space or down a wire is the distance between corresponding points (adjacent crests) in adjacent cycles. This length is commonly stated in metres (m), centimetres (cm), or millimetres (mm) in wireless systems (mm).

Find the count of brightdark-bright fringe shift

The number of lines will be determined by the formula presented in Challenge Example $22.9$.

$\mathrm{\Delta }m=(n-1)\frac{2d}{\lambda }$

We will have in our numerical case

$\mathrm{\Delta }m=0.00028X\frac{2X0.02m}{6X{10}^{-7}m}$

$∆m=\underset{\_}{18.7cm}$

It is now up to each person to decide whether or not it fits to round up above.