PHYS 463 Lab: Index of Refraction of Air

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.