14.5 Thin Film Interference

• Thin film interference occurs when light waves reflect off both the top and bottom surfaces of a thin film
• Match the type of interference with its condition:

  Constructive ↔️ \(2d = m\lambda\)

  Destructive ↔️ \(2d = (m + \frac{1}{2})\lambda\)
• The path difference in thin film interference is given by $2d =$$m\lambda$


  True
• The condition for destructive interference in thin films is $2d =$$m\lambda$, which requires a phase reversal
• A 180° phase shift occurs at a surface with a lower refractive index


  True
• For destructive interference with a phase shift, the condition is $2d =$$m\lambda$


  True
• What does the variable \(m\) represent in the path difference formula?

  An integer
• In the thin film interference formula, the thickness of the film is denoted by d
• How is the thin film thickness calculated if the wavelength and interference order are known?

  $d =$$\frac{(m + \frac{1}{2})\lambda}{2}$
• If a thin film has a thickness of 500 nm and the wavelength of light is 600 nm, the interference order is 1
• For constructive interference in thin films, the path difference is given by \(2d = m\lambda\), where \(d\) is the thickness
• For destructive interference in thin films, the path difference is given by \(2d = (m + \frac{1}{2})\lambda\), where \(m\) is an integer
• Match the reflection type with its phase shift:

  Lower refractive index ↔️ 180° (π radians)

  Higher refractive index ↔️ No phase shift
• Destructive interference in thin films results in reduced reflection due to a phase reversal upon reflection


  True
• Thin film interference occurs only with light waves


  True
• In the formula for path difference, \(d\) represents the thickness of the thin film
• The formula for thin film interference combines path difference and phase shift to determine interference conditions

  True
• What phase shift occurs at a surface with a higher refractive index?

  No phase shift
• Steps to derive the formula for thin film interference

  1️⃣ Consider the path difference between waves

  2️⃣ Account for phase shifts upon reflection

  3️⃣ Combine path difference and phase shift

  4️⃣ Derive the conditions for constructive and destructive interference
• A 180° phase shift occurs when light reflects at a surface with a lower refractive index


  True
• What does the variable \(\lambda\) represent in the thin film interference formula?

  Wavelength
• The formula for thin film interference is \(2d = (m + \frac{1}{2})\lambda\)
• The wavelength can be calculated using the formula \lambda = \frac{2d}{m + \frac{1}{2}}</latex>
• What is the interference order \(m\) if a thin film has a thickness of 500 nm and the wavelength of light is 600 nm?

  1
• The phase shift that occurs upon reflection depends on the refractive indices of the thin film and the surrounding media
• For constructive interference, the path difference is 2d
• The path difference between two reflected waves is given by 2d
• Match the interference type with its condition:

  Constructive ↔️ \(2d = (m + \frac{1}{2})\lambda\)

  Destructive ↔️ \(2d = m\lambda\)
• No phase shift occurs when light reflects at a surface with a higher refractive index


  True
• Steps to apply the thin film interference formula

  1️⃣ Identify the known variables

  2️⃣ Rearrange the formula if necessary

  3️⃣ Substitute the known values

  4️⃣ Calculate the unknown variable
• The interference order \(m\) can be negative

  False