Worksheet: Thin-Film Interference

In this worksheet, we will practice analyzing the interference of light reflected from parallel layers of substances with different refractive indices.

Q1:

A light wave that travels in a medium with a refractive index ๐‘›๏Šง is incident on and reflects from a medium with a refractive index ๐‘›๏Šจ. By how many degrees does the phase of the light wave change when it reflects if ๐‘›>๐‘›๏Šง๏Šจ?

Q2:

A light wave that travels in a medium with a refractive index ๐‘›๏Šง is incident on and reflects from a medium with a refractive index ๐‘›๏Šจ. By how many degrees does the phase of the light wave change when it reflects if ๐‘›<๐‘›๏Šง๏Šจ?

Q3:

A window is coated with an antireflective film 116 nm thick that has a refractive index of 1.24. For what wavelength of light does the film produce destructive interference?

  • A1.4ร—10๏Šฑ๏Šญ m
  • B11.6ร—10๏Šฑ๏Šญ m
  • C5.8ร—10๏Šฑ๏Šญ m
  • D2.9ร—10๏Šฑ๏Šญ m
  • E2.3ร—10๏Šฑ๏Šญ m

Q4:

A light wave travels in a medium with a refractive index ๐‘›๏Šง. The wave is incident on a surface of substance (a) that has refractive index ๐‘›๏Šจ. The wave is partially reflected and partially transmitted. The transmitted portion of the wave is incident on a surface of substance (b) that has a refractive index ๐‘›๏Šฉ, from which the wave is reflected. The incident wave, transmitted wave, and the two reflected waves are shown in the diagram. The refractive indices of the substances are ranked as follows: ๐‘›<๐‘›<๐‘›๏Šง๏Šจ๏Šฉ.

Does the phase of the light reflected from point A change on reflection?

  • ANo
  • BYes

Does the phase of the light reflected from point B change on reflection?

  • AYes
  • BNo

Q5:

A light wave travels in a medium with a refractive index ๐‘›๏Šง. The wave is incident on a surface of substance (a) that has refractive index ๐‘›๏Šจ. The wave is partially reflected and partially transmitted. The transmitted portion of the wave is incident on a surface of substance (b) that has a refractive index ๐‘›๏Šฉ, from which the wave is reflected. The incident wave, transmitted wave, and the two reflected waves are shown in the diagram. The refractive indices of the substances are ranked as follows: ๐‘›๏Šง < ๐‘›๏Šจ and ๐‘›๏Šฉ <๐‘›๏Šจ.

Does the phase of the light reflected from point A change on reflection?

  • AYes
  • BNo

Does the phase of the light reflected from point B change on reflection?

  • ANo
  • BYes

Q6:

The diagram shows the change of displacement with time for a light wave that is about to strike the top layer of a thin film. The blue plot shows the change of displacement with time for the portion of the wave that is reflected by the top layer of the thin film. The orange plot shows the change of displacement with time for the portion of the wave that is transmitted by the top layer of the thin film and then reflected from its bottom layer.

Does the substance above the film have a greater or smaller refractive index than the film?

  • AGreater
  • BSmaller

Does the substance below the film have a greater or smaller refractive index than the film?

  • ASmaller
  • BGreater

When the transmitted portion of the wave is reflected, is the reflection partial or total?

  • ATotal
  • BPartial

Q7:

A light wave of wavelength 430 nm travels in a medium with a refractive index ๐‘›๏Šง. The wave is incident on a surface of substance A that has a refractive index ๐‘›๏Šจ. The wave is partially reflected and partially transmitted. The transmitted portion of the wave is incident on a surface of substance B that has a refractive index ๐‘›๏Šฉ, from which the wave is partially reflected. The incident wave, the transmitted wave, and the two reflected waves are shown in the diagram. The angle of incidence of the light wave on substance A is 18โˆ˜, and the distance ๐‘‘ between the surfaces of substance A and substance B is 720 nm. The refractive indices are ๐‘›=1.0๏Šง, ๐‘›=1.55๏Šจ, and ๐‘›=1.25๏Šฉ. How many dark lines are observed in the interference pattern produced?

Q8:

A window is coated with a 110 nm thick antireflective film. The film is required to produce destructive interference for a 700 nm wavelength. What must the refractive index of the film be?

Q9:

A window is coated with an antireflective film that has a refractive index of 1.33. The film is required to produce destructive interference for a wavelength of 400 nm. What thickness of film must be applied?

  • A2.1ร—10๏Šฑ๏Šฎ m
  • B1.1ร—10๏Šฑ๏Šฎ m
  • C7.5ร—10๏Šฑ๏Šฎ m
  • D6.4ร—10๏Šฑ๏Šฎ m
  • E3.2ร—10๏Šฑ๏Šฎ m

Q10:

A light wave of wavelength 530 nm travels in a medium with a refractive index ๐‘›๏Šง. The wave is incident on a surface of substance ๐ด with a refractive index ๐‘›๏Šจ. The wave is partially reflected and partially transmitted. The transmitted portion of the wave is incident on a surface of substance ๐ต with a refractive index ๐‘›๏Šฉ, from which the wave is partially reflected. The incident wave, transmitted wave, and the two reflected waves are shown in the diagram. The angle of incidence of the light wave on substance ๐ด is 25โˆ˜. The refractive indices are ๐‘›=1.0๏Šง, ๐‘›=1.45๏Šจ, and ๐‘›=1.25๏Šฉ. Find the distance ๐‘‘ between the surfaces of substance ๐ด and substance ๐ต that results in three orders of constructive interference of reflected light.

  • A5.7ร—10๏Šฑ๏Šญ m
  • B4.3ร—10๏Šฑ๏Šญ m
  • C7.6ร—10๏Šฑ๏Šญ m
  • D1.9ร—10๏Šฑ๏Šญ m
  • E4.8ร—10๏Šฑ๏Šญ m

Q11:

A wave of sunlight travels in a medium with a refractive index ๐‘›๏Šง. The wave is incident on the surface of substance A that has a refractive index ๐‘›๏Šจ. The wave is partially reflected and partially transmitted, and the transmitted portion of it is incident on the surface of substance B that has a refractive index ๐‘›๏Šฉ from which the wave is partially reflected. The incident wave, the transmitted wave, and the two reflected waves are shown in the diagram. The distance ๐‘‘ between the surfaces of substance A and substance B is 250 nm, and the angle of incidence of the light wave on substance A is 35โˆ˜. The refractive indices ๐‘›=1.0๏Šง, ๐‘›=1.35๏Šจ, and ๐‘›=1.25๏Šฉ.

For what wavelength will the first order of reflected light interfere constructively?

  • A5.5ร—10๏Šฑ๏Šฌ m
  • B6.1ร—10๏Šฑ๏Šฌ m
  • C1.5ร—10๏Šฑ๏Šญ m
  • D1.2ร—10๏Šฑ๏Šฌ m
  • E3.1ร—10๏Šฑ๏Šญ m

For what wavelength will the first order of reflected light interfere destructively?

  • A12ร—10๏Šฑ๏Šญ m
  • B4.1ร—10๏Šฑ๏Šญ m
  • C3.1ร—10๏Šฑ๏Šญ m
  • D4.6ร—10๏Šฑ๏Šญ m
  • E6.1ร—10๏Šฑ๏Šญ m

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.