# Worksheet: Thin Film Interference

In this worksheet, we will practice calculating the thickness of thin films that produce interference by the reflection of light from the layers’ surfaces.

Q1:

A thin film with a refractive index of 1.32 is surrounded by air. What is the minimum thickness of this film that minimizes the reflection of normally incident light of wavelength 500 nm?

Q2:

After a minor oil spill, a thin film of oil, with a thickness of 450 nm, floats on the surface of the water in a bay. Use a value of 1.40 for the refractive index of the oil, and a value of 1.33 for the refractive index of the water. What is the predominant wavelength seen by someone flying in a helicopter overhead?

Q3:

A transparent film of thickness 250 nm and index of refraction 1.40 is surrounded by air. A beam of white light that is incident almost normal to the film undergoes destructive interference when reflected. What wavelength in the beam undergoes destructive interference at reflection from the film?

Q4:

A film of oil that has a refractive index of 1.40 floating on water will appear dark when it is very thin because the path length difference between the upper and lower boundaries of the film becomes small compared with the wavelength of light and there is a phase shift at the top surface. If the film of oil on some water becomes dark when the path length difference between the film’s upper and lower boundaries is less than one-fourth of the wavelength, what is the thickest the oil can be and appear dark at all visible wavelengths?

Q5:

A good-quality camera lens is actually a system of lenses, rather than a single lens, but a side effect is that a reflection from the surface of one lens can bounce around many times within the system, creating artifacts in the photograph. To counteract this problem, one of the lenses in such a system is coated with a thin layer of material with a refractive index on one side. The index of refraction of the lens glass is 1.68. What is the smallest thickness of the coating that reduces the reflection at 640 nm by destructive interference? (In other words, the coating’s effect is to be optimized for .)

Q6:

A lens is coated with fluorite. What is the second thinnest coating of fluorite that is nonreflective for m-wavelength light? Use 1.43 as the value of refractive index of fluorite.

Q7:

A soap bubble is blown outdoors in bright sunlight. What two visible wavelengths of the sunlight are most intensely reflected from the bubble? The soap bubble has a refractive index of 1.36 and the thickness of its skin is 380 nm.

• A421 nm and 642 nm
• B430 nm and 696 nm
• C413 nm and 689 nm
• D411 nm and 659 nm
• E408 nm and 675 nm

Q8:

A soap bubble is m thick and has a refractive index of 1.33. The bubble is illuminated by white light incident perpendicular to its surface. What wavelength of visible light is most constructively reflected from the bubble?

Q9:

Oil of refractive index 1.40 forms a slick that floats on water of refractive index 1.33. The oil slick is illuminated by white light perpendicular to its surface. What is the thickness of the slick if light of wavelength 470 nm is strongly reflected from it?

Q10:

Two identical pieces of rectangular plate glass are used to measure the thickness of a hair. The glass plates are in direct contact at one edge and a single hair is placed between them near the opposite edge. When illuminated with a light from a sodium lamp that has a wavelength , the hair is seen between the 180th and 181st dark fringes.

What is the lower limit of the hair’s diameter?

What is the upper limit of the hair’s diameter?

Q11:

Find the minimum thickness of a soap bubble that strongly reflects 680 nm wavelength light when illuminated by white light perpendicular to its surface. Use a value of 1.33 for the refractive index of the soap bubble.

Q12:

What are the smallest nonzero thicknesses of a film of soapy water on Plexiglas that strongly reflects 520 nm wavelength light when illuminated perpendicularly by white light? Use a value of 1.33 for the refractive index of the soapy water.

Q13:

As a soap bubble thins, it becomes darker because the path length difference between reflected light waves becomes small compared with the wavelength of light reflected by the bubble, and the light waves are phase-shifted at the top surface of the bubble. If the bubble becomes dark when the path length difference is less than one-fifth of the wavelength, what is the thickest the bubble can be and still appear dark at all visible wavelengths? Use a value of 575 nm for the reflected light’s wavelength and a value of 1.33 for the refractive index of the bubble.

Q14:

An intensity minimum is found for 380 nm light transmitted through a transparent film in air. The film has a refractive index of 1.2.

What is the minimum thickness of the film?

If 380 nm is the longest wavelength for which an intensity minimum occurs, what is the nearest wavelength to 380 nm that produces an intensity minimum?

Q15:

A thin film with a refractive index of 1.52 is surrounded by air. What is the minimum thickness of this film that results in the minimization of reflected 540 nm light when such light is normally incident on the bubble?

Q16:

Constructive interference is observed directly above an oil slick for wavelengths of 450 nm and 620 nm in air. The refractive index of the oil is 1.54. What is the film’s minimum possible thickness?

Q17:

Monochromatic light of wavelength 589 nm is perpendicularly incident on two glass slides. The top slide touches the bottom slide at one end and rests on a 0.250 mm diameter hair at the other end, forming a wedge of air. How far apart are the dark bands in the resulting interference pattern if the slides are 6.50 cm long?

Q18:

A soap bubble is 130 nm thick and illuminated by white light incident at a angle to its surface. What wavelength of visible light is most constructively reflected from the bubble? Use a value of 1.33 for the refractive index of the soap bubble.

Q19:

Two microscope slides made of glass are illuminated by monochromatic light of wavelength 589 nm that is incident vertically downward. The top slide touches the bottom slide at one end and rests on a thin copper wire at the other, forming a wedge of air. The diameter of the copper wire is 35.7 μm. How many bright fringes are seen across these slides if the refractive index of glass in the slides is 1.52?

Q20:

A microscope slide 13.0 cm long is separated from a glass plate at one end by a sheet of paper, with its other end in contact with the plate, as shown in the diagram. The slide is illuminated from vertically above by light from a sodium lamp of wavelength 589 nm, and 14.0 fringes per centimeter are seen along the slide. What is the thickness of the piece of paper if the refractive index of glass is 1.52?