PHYS 463 Lab: Index of Refraction of Air

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Questions and Answers

What happens to the path length when the refractive index changes by ∆n?

It changes by ∆n/2L

It changes by ∆nL

It does not change

It changes by 2∆nL (correct)

How many fringes will shift when the refractive index changes by ∆n = λ/2L?

Four fringes

One fringe (correct)

Three fringes

Two fringes

Which equation relates the number of fringes shifted to the change in pressure?

∆n/∆p = 2mλ/L

∆n/∆p = m/λ

∆n/∆p = 2L/mλ

∆n/∆p = mλ/2L (correct)

What does the variable k represent in the refractive index equation for air?

Constant relating refractive index and pressure Signup and view all the answers

How can the refractive index of air at room temperature be calculated?

Using n = 1 + mλp/2L∆p Signup and view all the answers

What occurs as air is removed from the interferometer?

The fringe pattern shifts Signup and view all the answers

Which step is NOT included in the procedure outlined for the experiment?

Directly touch the mirrors to adjust them Signup and view all the answers

What happens to the refractive index for most gases as the pressure increases?

It increases Signup and view all the answers

What is the main purpose of the experiment described?

To measure the index of refraction of air Signup and view all the answers

How is the optical path length of one beam calculated in the experiment?

By using the formula $2nL$ Signup and view all the answers

What happens to the interference pattern when the optical path length changes by one wavelength?

The pattern shifts by one fringe Signup and view all the answers

Which factor affects the optical path length in one of the beams during the experiment?

The pressure of the air in the cell Signup and view all the answers

What type of laser is used in the experiment to measure the index of refraction?

Helium-neon laser Signup and view all the answers

In the Michelson interferometer, what causes the bright regions in the interference pattern?

Crests of the wave arriving together Signup and view all the answers

What action is taken to change the refractive index of the air in the cell?

Remove the air from the cell Signup and view all the answers

Which instrument is primarily used in this experiment?

Michelson interferometer Signup and view all the answers

Study Notes

Purpose and Theory

The goal is to measure the index of refraction of air using a Michelson interferometer.
Optical path lengths of two air columns with the same physical length but at different pressures are compared.
Michelson interferometer utilizes a helium-neon laser to split a beam of light through a glass plate at a 45º angle.

Interferometer Functionality

Light from the laser is split into two beams; one travels to mirror M1, the other goes through the glass plate to mirror M2.
Beams are reflected back and combined to create an interference pattern on a screen.
The pattern consists of bright and dark concentric circles due to constructive and destructive interference of wave crests and troughs.

Optical Path Length

Optical path length is determined by the formula: ( nL ), with ( n ) as the index of refraction and ( L ) as the physical length.
The optical path length of the beam passing through the cell is ( 2nL ) since it traverses the cell twice.

Fringes and Index of Refraction

A shift in the interference pattern, or fringe, occurs if the optical path length changes by one wavelength.
Change in refractive index ( \Delta n ) is given by ( \Delta n = \frac{\lambda}{2L} ).
A shift of ( m ) fringes corresponds to a change: ( \Delta n = \frac{m\lambda}{2L} ).

Refractive Index of Air

For gases like air, the refractive index approaches 1, increasing proportionally with pressure.
The refractive index is expressed as: ( n = 1 + kp ), where ( p ) is pressure and ( k ) is an unknown constant.
The change in refractive index with pressure change is: ( \Delta n = k \Delta p ).

Relation Between Fringes and Pressure

Relation established between fringe shift ( m ) and pressure change ( \Delta p ):
( \frac{\Delta n}{\Delta p} = \frac{m\lambda}{2Lk} ).
Constant ( k ) can be defined as: ( k = \frac{m\lambda}{2L\Delta p} ).

Calculation of Refractive Index

The index of refraction at room temperature can be calculated with:
( n = 1 + \frac{m\lambda p}{2L\Delta p} ).

Experiment Instructions

Handle the Michelson interferometer components with care; do not touch glass surfaces.
Use a tube pump to withdraw air from the cell while ensuring all outlets are closed initially.
Gradually reduce air pressure and record the measurement once atmospheric pressure is regained.
Maintain airflow until the lowest pressure achievable is recorded.

Apparatus

Required instruments include a Michelson interferometer, helium-neon laser, air cell, and an exhaust fan with a pressure indicator.

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Description

This quiz focuses on determining the index of refraction of air utilizing a Michelson interferometer. By comparing optical path lengths in varying pressures, the experiment aims to provide insights into the properties of air. Dive into the principles of wave optics and the instrumental techniques used in this analysis.