# Worksheet: Interferometry

In this worksheet, we will practice calculating the characteristics of an interference pattern produced by two beams of light traveling along different paths.

Q1:

An experimenter detects 251 fringes when the movable mirror in a Michelson interferometer is displaced. The light source used is a sodium lamp, which emits light with a characteristic wavelength of 589 nm. By what distance did the movable mirror move?

Q2:

What is the distance moved by the traveling mirror of a Michelson interferometer that corresponds to 1,500 fringes passing by a point of the observation screen? Assume that the interferometer is illuminated with a 606 nm spectral line of krypton-86.

• A m
• B m
• C m
• D m
• E m

Q3:

A rectangular glass chamber that is 5.08 cm long is inserted into one arm of a Michelson interferometer using a 633 nm light source. This chamber is initially filled with air at standard atmospheric pressure. The air is gradually pumped out using a vacuum pump until the air pressure becomes negligible. How many fringes are observed moving by during the transition?

Q4:

In a Michelson interferometer, light of wavelength 632.8 nm from a laser is used. When one of the mirrors is moved by a distance , 8 fringes move past the field of view. What is the value of the distance ?

• A
• B
• C
• D
• E

Q5:

In a thermally stabilized lab, a Michelson interferometer is used to monitor the temperature to ensure it stays constant. The movable mirror is mounted on the end of an aluminum rod of length 1.00 m, held fixed at the other end. The light source is a laser, . The resolution of this apparatus corresponds to the temperature difference when a change of just one fringe is observed. Find the temperature difference. Use a value of for the thermal expansion coefficient of aluminum.

Q6:

A microscope slide is 10.0 cm long. One end of the slide is separated from a glass plate by a sheet of paper, while the other end of the slide is in contact with the glass plate. The slide is illuminated from directly above by light from a sodium lamp that has a wavelength . A fringe pattern is seen along the slide, the pattern contains 14 fringes per centimeter. The slide is then immersed in an unknown liquid. When immersed in the liquid, 18 fringes per centimeter are observed. What is the liquid’s refractive index? Q7:

A Michelson interferometer has two arms of equal length. A mercury light of wavelength 546 nm is used for the interferometer and stable fringes are observed. One of the arms is moved by 2.2 μm. How many fringes will cross the observing field? State your answer to the nearest fringe.

Q8:

When the traveling mirror of a Michelson interferometer is moved m, exactly 95 fringes pass by a point on the observation screen. What is the wavelength of the light used? Give your answer to three significant figures.

Q9:

A chamber 6.3 cm long with flat parallel windows at its ends is placed in one arm of a Michelson interferometer. The light used has a wavelength of 500 nm in vacuum. While all the air is being pumped out of the chamber, 32 fringes pass by a point on the observation screen. What is the refractive index of air? Write the answer to six significant figures.

Q10:

A Michelson interferometer with a He-Ne laser light source of wavelength 633 nm projects its interference pattern onto a screen. If the movable mirror is moved through a 9.34 μm displacement, how many fringes will be observed shifting through a reference point on the screen?

Q11:

A Michelson interferometer is used to measure the wavelength of light passing through it. When the movable mirror in the interferometer is displaced by 0.230 mm, the number of moving fringes observed is 284. What is the wavelength of the light?

Q12:

A plastic sheet of thickness 83.0 μm is inserted into one arm of a Michelson interferometer, causing a shift in the interference pattern by 90.0 fringes. The light source has a wavelength of 610 nm in air. What is the refractive index of the plastic?

Q13:

A 70 fringe shift is produced in a Michelson interferometer when a 48.0 μm thick film made of an unknown material is placed in one arm of the interferometer. The light source used has wavelength 633 nm. What is the refractive index of the unknown material?