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What will happen to Newton Ring if plate is silvered from back?

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Newton's rings are a pattern of alternating bright and dark concentric rings produced due to the interference of light waves reflected from the top and bottom surfaces of a thin air film, which is formed between a convex lens and a flat glass plate. The phenomenon is based on constructive and destructive interference.

If the **plate is silvered on the back surface**, the situation changes significantly. Let’s analyze this step by step:

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### 1. **Original Path of Reflection**
Normally, in Newton's ring setup:
- Light is incident on the system.
- A portion of the light reflects from the top surface of the air film (convex lens surface).
- Another portion of the light transmits through the air film, reflects off the flat glass plate surface (bottom of the air film), and comes back.
- These two reflected waves interfere to form the Newton’s rings.

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### 2. **What Happens When the Plate is Silvered?**
When the back surface of the flat glass plate is silvered:
- Almost all the transmitted light is reflected back (because the silvered surface is highly reflective).
- This creates a second reflected beam, which is superimposed on the original interference pattern.
- As a result, light undergoes **multiple reflections** inside the air film, leading to more complex interference.

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### 3. **Impact on the Newton's Rings Pattern**
The silvered surface alters the interference pattern in the following ways:

#### **(a) Increased Intensity of Rings**
- Due to the silvering, the second reflected beam is much stronger because it reflects almost completely from the silvered surface.
- As a result, the contrast and intensity of the Newton’s rings increase.

#### **(b) Superposition of Multiple Interference Patterns**
- Multiple reflections occur due to light bouncing back and forth between the surfaces (convex lens surface, air film, and silvered plate).
- This leads to the formation of overlapping interference patterns, which might blur or distort the clear visibility of the concentric rings.

#### **(c) Slight Phase Change Due to Reflection**
- Silvering introduces an additional phase change (depending on the reflective coating). This phase shift may slightly shift the positions of the bright and dark rings.

#### **(d) Absence of Transmitted Light**
- In the original Newton's rings setup, some light transmits through the flat plate. After silvering, this transmission is blocked, and the entire phenomenon depends only on reflected light.

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### 4. **Practical Consequences**
If you are observing Newton's rings:
- The rings will appear **brighter** and **more intense**.
- However, the pattern may also become more complex or distorted due to overlapping multiple reflections.
- If perfectly silvered, the secondary reflections can interfere constructively or destructively in unpredictable ways, depending on the exact thickness of the air film.

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### 5. **Special Case: Very Thin Films**
If the air film is extremely thin (e.g., near the center of the Newton’s rings pattern), the effect of multiple reflections will become even more pronounced. This could lead to significant deviations from the usual Newton's rings appearance.

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### Conclusion
Silvering the back of the flat glass plate increases the intensity of Newton’s rings but may distort their clarity due to the superposition of multiple reflected light waves. The visibility and sharpness of the rings depend on the quality of the silvering and the alignment of the system.
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