An infinitely thick sheet of glass (ng = 1.5) is coated with a 500-nm thick layer of oil (noil = 1.42). a) For what visible wavelengths of light (400 nm-700 nm) do the reflected waves initially incident on the oil layer undergo maximum constructive interference? b) For what visible wavelengths of light (400 nm-700 nm) do the reflected waves initially incident on the oil layer undergo perfect destructive interference? **see image for properly formatted question** ### Interference of Light Waves - Educational Breakdown#### Problem Statement1. An infinitely thick sheet of glass (\( n_g = 1.5 \)) is coated with a 500-nm thick layer of oil (\( n_{\text{oil}} = 1.42 \)).**Questions:**a. For what visible wavelengths of light (400 nm - 700 nm) do the reflected waves initially incident on the oil layer undergo maximum constructive interference?b. For what visible wavelengths of light (400 nm - 700 nm) do the reflected waves initially incident on the oil layer undergo perfect destructive interference?#### Concepts and Background:When light waves reflect off a thin film of material, interference patterns arise due to the difference in the path lengths traveled by the reflected rays. This can lead to either constructive or destructive interference depending on the phase difference between the waves.- **Constructive Interference:** Occurs when the path difference between the two waves is an integer multiple of the wavelength (e.g. \( m\lambda \), where \( m \) is an integer). - **Destructive Interference:** Occurs when the path difference between the two waves is an odd integer multiple of half the wavelength (e.g. \( (m + \frac{1}{2})\lambda \)).#### Detailed Analysis:1. **Determining the Reflected Wave Behavior:** - Light reflecting off the top surface of the oil experiences a phase change of \( 180^\circ \). - Light reflecting off the oil-glass interface experiences no phase change if the refractive index of oil \( n_{\text{oil}} \) is less than that of the glass \( n_g \).**Formulas**:- **Constructive Interference:** \[ 2t = m\frac{\lambda}{n_{\text{oil}}} \] Simplified for maximum constructive interference within the given wavelength range: \[ \lambda = \frac{2t \cdot n_{\text{oil}}}{m} \]- **Destructive Interference:** \[ 2t = (m + \frac{1}{2})\frac{\lambda}{n_{\text{oil}}} \] Simplified for perfect destructive interference within the given wavelength range: \[ \lambda = \frac{2t \cdot n_{\text{oil ### Material Properties TableThe table below summarizes various physical properties for selected materials. This data is crucial for understanding thermal and physical behavior in educational and engineering contexts.| Material | α (°C−1) | c (J/(kg K)) | C (J/(mol K)) | Lf (J/kg) | Lv (J/kg) | density (kg/m3) ||------------------|---------------------|--------------|---------------|----------------------|----------------------|---------------------------|| Gold | - | 129 | 25 | - | - | 19,300 || Copper | 1.65×10−5| - | - | - | - | 8,960 || Aluminum | 2.3×10−5 | - | - | - | - | 2,700 || Stainless Steel | 1.75×10−5| - | - | - | - | 7,500 || Water | - | 4190 | 75 | 3.33×105 | 22.6×105 | 1,000 || Ethyl Alcohol | - | 2400 | 110 | 1.09×105 | 8.79×105 | 790 || Ice | - | 2090 | 37.6 | - | - | 917 |#### Constants- **1 atm** = 1.01×105 Pa- **NA** = 6.022×1023 particles/mol- **R** = 8.3145 J/(mol K)- **kB** = 1.38×10−23 J/K- **σ** = 5.67 × 10

Given: The refractive index of glass is 1.5. The refractive index of oil is 1.42.…

An infinitely thick sheet of glass (n = 1.5) is coated with a 500-nm thick layer of oil (noil = 1.42). a. For what visible wavelengths of light (400 nm-700 nm) do the reflected waves initially incident on the oil layer undergo maximum constructive interference? B. For what visible wavelengths of light (400 nm-700 nm) do the reflected waves initially incident on the oil layer undergo perfect destructive interference?

An infinitely thick sheet of glass (n = 1.5) is coated with a 500-nm thick layer of oil (noil = 1.42). a. For what visible wavelengths of light (400 nm-700 nm) do the reflected waves initially incident on the oil layer undergo maximum constructive interference? B. For what visible wavelengths of light (400 nm-700 nm) do the reflected waves initially incident on the oil layer undergo perfect destructive interference?

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