To solve the problem of determining which color of light will have minimum reflection for a silicon solar cell coated with silicon dioxide, we need to consider the phenomenon of destructive interference. In this context, the minimum reflection occurs at specific wavelengths determined by the thickness of the coating and the refractive index of the material.
1. Given Data:
- Refractive index of silicon ([tex]\( n_{\text{silicon}} \)[/tex]): [tex]\( 3.50 \)[/tex]
- Refractive index of silicon dioxide ([tex]\( n_{\text{SiO}_2} \)[/tex]): [tex]\( 1.45 \)[/tex]
- Thickness of silicon dioxide layer ([tex]\( d \)[/tex]): [tex]\( 214 \, \text{nm} \)[/tex]
2. Formula:
The wavelength of minimum reflection ([tex]\(\lambda\)[/tex]) for a single-layer antireflective coating is given by the condition:
[tex]\[
\lambda = 4 \times n \times d
\][/tex]
where [tex]\( n \)[/tex] is the refractive index of the coating material (silicon dioxide in this case) and [tex]\( d \)[/tex] is the thickness of the coating.
3. Calculation:
Substitute the given values into the formula:
[tex]\[
\lambda = 4 \times 1.45 \times 214 \, \text{nm}
\][/tex]
Perform the multiplication:
[tex]\[
\lambda = 4 \times 1.45 \times 214 = 1241.2 \, \text{nm}
\][/tex]
4. Comparison with Visible Light Wavelengths:
The visible light spectrum ranges approximately from 400 nm to 700 nm. According to the given information, the wavelength ranges for different colors are:
- Violet: [tex]\(400 \, \text{nm} - 450 \, \text{nm}\)[/tex]
- Blue: [tex]\(450 \, \text{nm} - 495 \, \text{nm}\)[/tex]
- Green: [tex]\(495 \, \text{nm} - 570 \, \text{nm}\)[/tex]
- Yellow: [tex]\(570 \, \text{nm} - 590 \, \text{nm}\)[/tex]
- Orange: [tex]\(590 \, \text{nm} - 620 \, \text{nm}\)[/tex]
- Red: [tex]\(620 \, \text{nm} - 700 \, \text{nm}\)[/tex]
5. Conclusion:
The calculated wavelength for minimum reflection is [tex]\( 1241.2 \, \text{nm} \)[/tex], which lies outside the visible light spectrum (400 nm to 700 nm). Therefore, none of the visible light colors (Violet, Blue, Green, Yellow, Orange, Red) will experience minimum reflection.
Thus, based on the given properties of the materials and the thickness of the coating layer, there is no visible light color that will have minimum reflection for this silicon solar cell.
