Question

What is antireflection coating? Deduce an expression for the minimum thickness of the antireflection coating.

Answer 1

### **What is Antireflection Coating?**

Antireflection coating is a thin layer of material applied to the surface of lenses, screens, or glass to reduce the reflection of light. This helps more light pass through the surface, improving visibility and reducing glare. It is widely used in optical devices like camera lenses, glasses, and solar panels to enhance efficiency.

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### **Principle of Antireflection Coating**

- The coating works on the principle of **destructive interference**.
- When light is reflected from the two surfaces of the thin coating (air-coating interface and coating-glass interface), the reflected rays cancel each other out.
- This happens when the optical path difference between the reflected rays is equal to half the wavelength (\( \lambda/2 \)).

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### **Expression for Minimum Thickness**

To achieve destructive interference, the optical path difference between the two reflected rays must satisfy the following condition:

\[
2 \mu t = \frac{\lambda}{2}
\]

Where:  
- \( \mu \) = Refractive index of the antireflection coating  
- \( t \) = Thickness of the antireflection coating (to be calculated)  
- \( \lambda \) = Wavelength of light  

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#### **Step-by-Step Deduction**:

1. **Path Difference**:  
   The light ray travels twice through the coating (downward and upward), so the path difference is \( 2 \mu t \).

2. **Condition for Destructive Interference**:  
   For destructive interference to occur, the path difference must equal \( \lambda/2 \), where \( \lambda \) is the wavelength of light in air.  

   Thus,  
   \[
   2 \mu t = \frac{\lambda}{2}
   \]

3. **Solve for Thickness (\( t \))**:  
   Rearrange the formula to find \( t \):  
   \[
   t = \frac{\lambda}{4 \mu}
   \]

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### **Final Expression**:
The minimum thickness of the antireflection coating is:  
\[
t = \frac{\lambda}{4 \mu}
\]

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### **Key Points to Memorize**:
1. **Purpose**: Reduces reflection and enhances light transmission.  
2. **Principle**: Based on **destructive interference**.  
3. **Formula**: Minimum thickness \( t = \frac{\lambda}{4 \mu} \).  
4. **Applications**: Used in optical devices like glasses, microscopes, and solar panels.  

This explanation and formula will ensure you get full marks for the answer!