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*Chapter 35, Problem 058 Transmission through thin layers. In the figure, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) Part of the light ends up in material 3 as ray r3 (the light does not reflect inside material 2) and r4 (the light reflects twice inside material 2). The waves of r3 and r4 interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). The table below provides the indexes of refraction n1, n2, and n3, the type of interference, and the wavelength A in nanometers of the light as measured in air. Give the third least thickness L.

*Chapter 35, Problem 058 Transmission through thin layers. In the figure, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) Part of the light ends up in material 3 as ray r3 (the light does not reflect inside material 2) and r4 (the light reflects twice inside material 2). The waves of r3 and r4 interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). The table below provides the indexes of refraction n1, n2, and n3, the type of interference, and the wavelength A in nanometers of the light as measured in air. Give the third least thickness L.

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## Chapter 35, Problem 058 ### Transmission through thin layers In the figure, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) Part of the light ends up in material 3 as ray \( r_3 \) (the light does not reflect inside material 2) and \( r_4 \) (the light reflects twice inside material 2). The waves of \( r_3 \) and \( r_4 \) interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). The table below provides the indexes of refraction \( n_1 \), \( n_2 \), and \( n_3 \), the type of interference and the wavelength \( \lambda \) in nanometers of the light as measured in air. Give the third least thickness \( L \). #### Figure Explanation The figure consists of a diagram illustrating the perpendicular incidence of light on a thin layer (material 2) which is sandwiched between two thicker materials (material 1 and material 3). Here is a detailed breakdown of the diagram: - Materials are labeled as: - \( n_1 \) for material 1 - \( n_2 \) for material 2 - \( n_3 \) for material 3 - The path of light incidence is shown as ray \( i \) entering material 2. - Ray \( r_3 \) represents the light ray that does not reflect and continues into material 3. - Ray \( r_4 \) represents the light ray that reflects twice within material 2 before emerging into material 3. - The thickness of material 2 is denoted as \( L \). #### Table Information | \( n_1 \) | \( n_2 \) | \( n_3 \) | Type | \( L \) | \( \lambda \) (nm) | |-----------|-----------|-----------|------|--------|--------------------| | 1.37 | 1.84 | 1.45 | min | 3rd | 384 | Please calculate the third least thickness \( L \) based on the provided data and principles of light interference.
Transcribed Image Text:## Chapter 35, Problem 058 ### Transmission through thin layers In the figure, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) Part of the light ends up in material 3 as ray \( r_3 \) (the light does not reflect inside material 2) and \( r_4 \) (the light reflects twice inside material 2). The waves of \( r_3 \) and \( r_4 \) interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). The table below provides the indexes of refraction \( n_1 \), \( n_2 \), and \( n_3 \), the type of interference and the wavelength \( \lambda \) in nanometers of the light as measured in air. Give the third least thickness \( L \). #### Figure Explanation The figure consists of a diagram illustrating the perpendicular incidence of light on a thin layer (material 2) which is sandwiched between two thicker materials (material 1 and material 3). Here is a detailed breakdown of the diagram: - Materials are labeled as: - \( n_1 \) for material 1 - \( n_2 \) for material 2 - \( n_3 \) for material 3 - The path of light incidence is shown as ray \( i \) entering material 2. - Ray \( r_3 \) represents the light ray that does not reflect and continues into material 3. - Ray \( r_4 \) represents the light ray that reflects twice within material 2 before emerging into material 3. - The thickness of material 2 is denoted as \( L \). #### Table Information | \( n_1 \) | \( n_2 \) | \( n_3 \) | Type | \( L \) | \( \lambda \) (nm) | |-----------|-----------|-----------|------|--------|--------------------| | 1.37 | 1.84 | 1.45 | min | 3rd | 384 | Please calculate the third least thickness \( L \) based on the provided data and principles of light interference.
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